home *** CD-ROM | disk | FTP | other *** search
| Unknown | 1997-01-27 | 14.9 KB |
open in: 
MacOS 8.1
|
Win98
|
DOS
view JSON data
|
view as text
This file was not able to be converted.
This format is not currently supported by dexvert.
| Confidence | Program | Detection | Match Type | Support
|
|---|
| 1%
| dexvert
| Eclipse Tutorial (other/eclipseTutorial)
| ext
| Unsupported |
| 1%
| dexvert
| JuggleKrazy Tutorial (other/juggleKrazyTutorial)
| ext
| Unsupported |
| 100%
| file
| data
| default
| |
| 100%
| gt2
| Kopftext: 'TUTOR 06'
| default (weak)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 54 55 54 4f 52 20 30 36 | df 36 00 00 a8 04 00 00 |TUTOR 06|.6......|
|00000010| 00 17 4f 04 0d 0b 00 4e | 6f 2e 20 20 59 6f 75 20 |..O....N|o. You |
|00000020| 73 68 6f 75 6c 64 20 68 | 61 76 65 20 75 73 65 64 |should h|ave used|
|00000030| 20 74 68 65 20 73 75 6d | 20 66 6f 72 6d 75 6c 61 | the sum| formula|
|00000040| 2c 20 0d 0a 00 63 6f 73 | 28 11 33 75 20 11 31 2b |, ...cos|(.3u .1+|
|00000050| 20 11 33 76 11 31 29 20 | 3d 20 63 6f 73 20 11 33 | .3v.1) |= cos .3|
|00000060| 75 20 11 31 63 6f 73 20 | 11 33 76 20 11 31 2d 20 |u .1cos |.3v .1- |
|00000070| 73 69 6e 20 11 33 75 20 | 11 31 73 69 6e 20 11 33 |sin .3u |.1sin .3|
|00000080| 76 11 31 2e 0d 0a 00 00 | 17 4f 05 0d 0b 00 47 6f |v.1.....|.O....Go|
|00000090| 6f 64 2e 20 20 53 69 6e | 63 65 20 63 6f 73 20 11 |od. Sin|ce cos .|
|000000a0| 33 75 20 11 31 63 6f 73 | 20 11 33 76 20 11 31 2d |3u .1cos| .3v .1-|
|000000b0| 20 73 69 6e 20 11 33 75 | 20 11 31 73 69 6e 20 11 | sin .3u| .1sin .|
|000000c0| 33 76 20 11 31 3d 20 63 | 6f 73 28 11 33 75 20 11 |3v .1= c|os(.3u .|
|000000d0| 31 2b 20 11 33 76 11 31 | 29 2c 20 74 68 65 6e 0d |1+ .3v.1|), then.|
|000000e0| 0a 00 20 20 20 20 20 20 | 11 34 6f 20 20 20 20 20 |.. |.4o |
|000000f0| 20 20 6f 20 20 20 20 20 | 20 20 20 20 6f 20 20 20 | o | o |
|00000100| 20 20 20 20 6f 20 20 20 | 20 20 20 20 20 20 6f 20 | o | o |
|00000110| 20 20 20 20 6f 20 20 20 | 20 20 20 20 20 20 20 6f | o | o|
|00000120| 0d 0b 00 11 31 63 6f 73 | 20 35 30 20 20 63 6f 73 |....1cos| 50 cos|
|00000130| 20 32 35 20 20 2d 20 73 | 69 6e 20 35 30 20 20 73 | 25 - s|in 50 s|
|00000140| 69 6e 20 32 35 20 20 3d | 20 63 6f 73 28 35 30 20 |in 25 =| cos(50 |
|00000150| 20 2b 20 32 35 20 29 20 | 3d 20 63 6f 73 20 37 35 | + 25 ) |= cos 75|
|00000160| 20 2e 0d 0a 00 00 17 4f | 05 20 20 20 20 20 20 20 | ......O|. |
|00000170| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000180| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000190| 20 20 20 20 20 20 20 20 | 20 20 11 34 6f 20 20 20 | | .4o |
|000001a0| 20 20 20 20 6f 0d 0b 00 | 11 31 57 72 6f 6e 67 2e | o...|.1Wrong.|
|000001b0| 20 20 59 6f 75 20 73 68 | 6f 75 6c 64 20 68 61 76 | You sh|ould hav|
|000001c0| 65 20 73 75 62 74 72 61 | 63 74 65 64 20 74 68 65 |e subtra|cted the|
|000001d0| 20 61 6e 67 6c 65 73 20 | 32 33 35 20 20 61 6e 64 | angles |235 and|
|000001e0| 20 36 38 20 20 73 69 6e | 63 65 0d 0a 00 0d 0b 00 | 68 sin|ce......|
|000001f0| 20 74 61 6e 20 11 33 75 | 20 11 31 2d 20 74 61 6e | tan .3u| .1- tan|
|00000200| 20 11 33 76 0d 0b 00 11 | 34 32 32 32 32 32 32 32 | .3v....|42222222|
|00000210| 32 32 32 32 32 32 32 32 | 20 11 31 3d 20 74 61 6e |22222222| .1= tan|
|00000220| 28 11 33 75 20 11 31 2d | 20 11 33 76 11 31 29 2e |(.3u .1-| .3v.1).|
|00000230| 0d 0b 00 31 20 2b 20 74 | 61 6e 20 11 33 75 20 11 |...1 + t|an .3u .|
|00000240| 31 74 61 6e 20 11 33 76 | 0d 0a 00 00 17 4f 04 0d |1tan .3v|.....O..|
|00000250| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00000260| 20 20 74 61 6e 20 11 33 | 75 20 11 31 2d 20 74 61 | tan .3|u .1- ta|
|00000270| 6e 20 11 33 76 0d 0b 00 | 11 31 43 6f 72 72 65 63 |n .3v...|.1Correc|
|00000280| 74 2c 20 73 69 6e 63 65 | 20 11 34 32 32 32 32 32 |t, since| .422222|
|00000290| 32 32 32 32 32 32 32 32 | 32 32 20 11 31 3d 20 74 |22222222|22 .1= t|
|000002a0| 61 6e 28 11 33 75 20 11 | 31 2d 20 11 33 76 11 31 |an(.3u .|1- .3v.1|
|000002b0| 29 2e 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |).... | |
|000002c0| 20 20 20 20 31 20 2b 20 | 74 61 6e 20 11 33 75 20 | 1 + |tan .3u |
|000002d0| 11 31 74 61 6e 20 11 33 | 76 0d 0a 00 00 17 4f 05 |.1tan .3|v.....O.|
|000002e0| 0d 0b 00 57 72 6f 6e 67 | 2e 20 20 49 20 74 68 69 |...Wrong|. I thi|
|000002f0| 6e 6b 20 79 6f 75 27 72 | 65 20 67 75 65 73 73 69 |nk you'r|e guessi|
|00000300| 6e 67 2e 20 20 55 73 65 | 20 74 68 65 20 66 6f 72 |ng. Use| the for|
|00000310| 6d 75 6c 61 20 0d 0a 00 | 0d 0b 00 20 74 61 6e 20 |mula ...|... tan |
|00000320| 11 33 75 20 11 31 2d 20 | 74 61 6e 20 11 33 76 0d |.3u .1- |tan .3v.|
|00000330| 0b 00 11 34 32 32 32 32 | 32 32 32 32 32 32 32 32 |...42222|22222222|
|00000340| 32 32 32 20 11 31 3d 20 | 74 61 6e 28 11 33 75 20 |222 .1= |tan(.3u |
|00000350| 11 31 2d 20 11 33 76 11 | 31 29 2e 0d 0b 00 31 20 |.1- .3v.|1)....1 |
|00000360| 2b 20 74 61 6e 20 11 33 | 75 20 11 31 74 61 6e 20 |+ tan .3|u .1tan |
|00000370| 11 33 76 0d 0a 00 00 17 | 4f 04 0d 0b 00 57 72 6f |.3v.....|O....Wro|
|00000380| 6e 67 2e 20 20 54 68 69 | 73 20 65 78 70 72 65 73 |ng. Thi|s expres|
|00000390| 73 69 6f 6e 20 63 61 6e | 20 62 65 20 73 69 6d 70 |sion can| be simp|
|000003a0| 6c 69 66 69 65 64 20 62 | 79 20 75 73 69 6e 67 20 |lified b|y using |
|000003b0| 74 68 65 20 64 69 66 66 | 65 72 65 6e 63 65 20 0d |the diff|erence .|
|000003c0| 0a 00 66 6f 72 6d 75 6c | 61 20 66 6f 72 20 74 61 |..formul|a for ta|
|000003d0| 6e 67 65 6e 74 2e 0d 0a | 00 00 17 4f 05 0d 0b 00 |ngent...|...O....|
|000003e0| 57 72 6f 6e 67 2e 20 20 | 57 68 79 20 64 69 64 20 |Wrong. |Why did |
|000003f0| 79 6f 75 20 6d 75 6c 74 | 69 70 6c 79 20 34 11 33 |you mult|iply 4.3|
|00000400| 78 20 11 31 61 6e 64 20 | 32 11 33 78 11 31 3f 20 |x .1and |2.3x.1? |
|00000410| 20 59 6f 75 20 73 68 6f | 75 6c 64 20 75 73 65 20 | You sho|uld use |
|00000420| 74 68 65 20 66 6f 72 6d | 75 6c 61 0d 0a 00 20 20 |the form|ula... |
|00000430| 20 20 20 20 20 20 20 20 | 20 20 20 20 74 61 6e 20 | | tan |
|00000440| 11 33 75 20 11 31 2b 20 | 74 61 6e 20 11 33 76 0d |.3u .1+ |tan .3v.|
|00000450| 0b 00 11 31 74 61 6e 28 | 11 33 75 20 11 31 2b 20 |...1tan(|.3u .1+ |
|00000460| 11 33 76 11 31 29 20 3d | 20 11 34 32 32 32 32 32 |.3v.1) =| .422222|
|00000470| 32 32 32 32 32 32 32 32 | 32 32 11 31 2e 0d 0b 00 |22222222|22.1....|
|00000480| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 31 20 2d | | 1 -|
|00000490| 20 74 61 6e 20 11 33 75 | 20 11 31 74 61 6e 20 11 | tan .3u| .1tan .|
|000004a0| 33 76 0d 0a 00 00 17 4f | 04 0d 0b 00 20 20 20 20 |3v.....O|.... |
|000004b0| 20 20 20 20 74 61 6e 20 | 34 11 33 78 20 11 31 2b | tan |4.3x .1+|
|000004c0| 20 74 61 6e 20 32 11 33 | 78 0d 0b 00 11 31 47 6f | tan 2.3|x....1Go|
|000004d0| 6f 64 2e 20 20 11 34 32 | 32 32 32 32 32 32 32 32 |od. .42|22222222|
|000004e0| 32 32 32 32 32 32 32 32 | 20 11 31 3d 20 74 61 6e |22222222| .1= tan|
|000004f0| 28 34 11 33 78 20 11 31 | 2b 20 32 11 33 78 11 31 |(4.3x .1|+ 2.3x.1|
|00000500| 29 20 3d 20 74 61 6e 20 | 36 11 33 78 11 31 2e 0d |) = tan |6.3x.1..|
|00000510| 0b 00 20 20 20 20 20 20 | 20 31 20 2d 20 74 61 6e |.. | 1 - tan|
|00000520| 20 34 11 33 78 20 11 31 | 74 61 6e 20 32 11 33 78 | 4.3x .1|tan 2.3x|
|00000530| 0d 0a 00 00 17 4f 04 0d | 0b 00 4e 6f 2e 20 20 59 |.....O..|..No. Y|
|00000540| 6f 75 20 73 68 6f 75 6c | 64 20 68 61 76 65 20 75 |ou shoul|d have u|
|00000550| 73 65 64 20 74 68 65 20 | 73 75 6d 20 66 6f 72 6d |sed the |sum form|
|00000560| 75 6c 61 20 66 6f 72 20 | 74 68 65 20 74 61 6e 67 |ula for |the tang|
|00000570| 65 6e 74 20 66 75 6e 63 | 74 69 6f 6e 2c 20 6e 6f |ent func|tion, no|
|00000580| 74 20 74 68 65 0d 0a 00 | 64 69 66 66 65 72 65 6e |t the...|differen|
|00000590| 63 65 20 66 6f 72 6d 75 | 6c 61 2e 0d 0a 00 00 17 |ce formu|la......|
|000005a0| 4f 05 0d 0b 00 53 6f 72 | 72 79 2c 20 62 75 74 20 |O....Sor|ry, but |
|000005b0| 74 68 69 73 20 63 61 6e | 20 62 65 20 73 69 6d 70 |this can| be simp|
|000005c0| 6c 69 66 69 65 64 2e 20 | 20 55 73 65 20 74 68 65 |lified. | Use the|
|000005d0| 20 66 6f 72 6d 75 6c 61 | 0d 0a 00 20 20 20 20 20 | formula|... |
|000005e0| 20 20 20 20 20 20 20 20 | 20 74 61 6e 20 11 33 75 | | tan .3u|
|000005f0| 20 11 31 2b 20 74 61 6e | 20 11 33 76 0d 0b 00 11 | .1+ tan| .3v....|
|00000600| 31 74 61 6e 28 11 33 75 | 20 11 31 2b 20 11 33 76 |1tan(.3u| .1+ .3v|
|00000610| 11 31 29 20 3d 20 11 34 | 32 32 32 32 32 32 32 32 |.1) = .4|22222222|
|00000620| 32 32 32 32 32 32 32 11 | 31 2e 0d 0b 00 20 20 20 |2222222.|1.... |
|00000630| 20 20 20 20 20 20 20 20 | 20 20 31 20 2d 20 74 61 | | 1 - ta|
|00000640| 6e 20 11 33 75 20 11 31 | 74 61 6e 20 11 33 76 0d |n .3u .1|tan .3v.|
|00000650| 0a 00 00 17 4f 08 20 20 | 20 20 20 20 20 20 20 20 |....O. | |
|00000660| 20 20 20 20 20 20 20 20 | 20 20 20 20 33 20 20 20 | | 3 |
|00000670| 20 20 20 20 20 20 20 20 | 20 20 11 34 70 20 20 20 | | .4p |
|00000680| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 31 34 0d | | .14.|
|00000690| 0b 00 57 72 6f 6e 67 2e | 20 20 53 69 6e 63 65 20 |..Wrong.| Since |
|000006a0| 73 69 6e 20 11 33 75 20 | 11 31 3d 20 11 34 32 20 |sin .3u |.1= .42 |
|000006b0| 11 31 61 6e 64 20 30 20 | 3c 20 11 33 75 20 11 31 |.1and 0 |< .3u .1|
|000006c0| 3c 20 11 34 32 11 31 2c | 20 74 68 65 6e 20 63 6f |< .42.1,| then co|
|000006d0| 73 20 11 33 75 20 11 31 | 3d 20 11 34 32 11 31 2c |s .3u .1|= .42.1,|
|000006e0| 20 61 6e 64 20 73 69 6e | 63 65 20 0d 0b 00 20 20 | and sin|ce ... |
|000006f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000700| 20 20 20 20 35 20 20 20 | 20 20 20 20 20 20 20 20 | 5 | |
|00000710| 20 20 32 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 2 | |
|00000720| 20 20 35 0d 0a 00 20 20 | 20 20 20 20 20 20 20 20 | 5... | |
|00000730| 35 20 20 20 20 20 11 34 | 70 20 20 20 20 20 20 20 |5 .4|p |
|00000740| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000750| 11 31 31 32 0d 0b 00 63 | 6f 73 20 11 33 76 20 11 |.112...c|os .3v .|
|00000760| 31 3d 20 2d 11 34 32 32 | 20 11 31 61 6e 64 20 11 |1= -.422| .1and .|
|00000770| 34 32 20 11 31 3c 20 11 | 33 76 20 11 31 3c 20 11 |42 .1< .|3v .1< .|
|00000780| 34 70 11 31 2c 20 74 68 | 65 6e 20 73 69 6e 20 11 |4p.1, th|en sin .|
|00000790| 33 76 20 11 31 3d 20 11 | 34 32 32 11 31 2e 20 20 |3v .1= .|422.1. |
|000007a0| 54 68 65 72 65 66 6f 72 | 65 2c 20 0d 0b 00 20 20 |Therefor|e, ... |
|000007b0| 20 20 20 20 20 20 20 31 | 33 20 20 20 20 20 32 20 | 1|3 2 |
|000007c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000007d0| 20 20 20 20 20 20 31 33 | 0d 0a 00 20 20 20 20 20 | 13|... |
|000007e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000007f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000800| 20 20 20 20 11 34 28 20 | 20 20 20 20 20 29 20 20 | .4( | ) |
|00000810| 20 28 20 20 20 20 20 20 | 20 29 0d 0b 00 20 20 20 | ( | )... |
|00000820| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000830| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000840| 20 20 20 20 20 20 21 11 | 31 31 32 20 20 20 34 11 | !.|112 4.|
|00000850| 34 21 20 20 20 21 20 20 | 11 31 35 20 20 20 33 11 |4! ! |.15 3.|
|00000860| 34 21 20 20 20 11 31 33 | 33 0d 0b 00 73 69 6e 28 |4! .13|3...sin(|
|00000870| 11 33 76 20 11 31 2b 20 | 11 33 75 11 31 29 20 3d |.3v .1+ |.3u.1) =|
|00000880| 20 73 69 6e 20 11 33 76 | 20 11 31 63 6f 73 20 11 | sin .3v| .1cos .|
|00000890| 33 75 20 11 31 2b 20 63 | 6f 73 20 11 33 76 20 11 |3u .1+ c|os .3v .|
|000008a0| 31 73 69 6e 20 11 33 75 | 20 11 31 3d 20 11 34 21 |1sin .3u| .1= .4!|
|000008b0| 32 32 20 2a 20 32 21 20 | 11 31 2b 20 11 34 21 11 |22 * 2! |.1+ .4!.|
|000008c0| 31 2d 11 34 32 32 20 2a | 20 32 21 20 11 31 3d 20 |1-.422 *| 2! .1= |
|000008d0| 11 34 32 32 11 31 2e 0d | 0b 00 20 20 20 20 20 20 |.422.1..|.. |
|000008e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000008f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000900| 20 20 20 11 34 21 11 31 | 31 33 20 20 20 35 11 34 | .4!.1|13 5.4|
|00000910| 21 20 20 20 21 20 11 31 | 31 33 20 20 20 35 11 34 |! ! .1|13 5.4|
|00000920| 21 20 20 20 11 31 36 35 | 0d 0b 00 20 20 20 20 20 |! .165|... |
|00000930| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000940| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000950| 20 20 20 20 11 34 39 20 | 20 20 20 20 20 30 20 20 | .49 | 0 |
|00000960| 20 39 20 20 20 20 20 20 | 20 30 0d 0a 00 00 17 4f | 9 | 0.....O|
|00000970| 04 0d 0b 00 57 72 6f 6e | 67 2e 20 20 49 20 74 68 |....Wron|g. I th|
|00000980| 69 6e 6b 20 79 6f 75 20 | 75 73 65 64 20 74 68 65 |ink you |used the|
|00000990| 20 77 72 6f 6e 67 20 66 | 6f 72 6d 75 6c 61 2e 20 | wrong f|ormula. |
|000009a0| 20 54 72 79 20 75 73 69 | 6e 67 20 74 68 65 20 66 | Try usi|ng the f|
|000009b0| 6f 72 6d 75 6c 61 0d 0a | 00 73 69 6e 28 11 33 76 |ormula..|.sin(.3v|
|000009c0| 20 11 31 2b 20 11 33 75 | 11 31 29 20 3d 20 73 69 | .1+ .3u|.1) = si|
|000009d0| 6e 20 11 33 76 20 11 31 | 63 6f 73 20 11 33 75 20 |n .3v .1|cos .3u |
|000009e0| 11 31 2b 20 63 6f 73 20 | 11 33 76 20 11 31 73 69 |.1+ cos |.3v .1si|
|000009f0| 6e 20 11 33 75 11 31 2e | 0d 0a 00 00 17 4f 03 0d |n .3u.1.|.....O..|
|00000a00| 0b 00 43 6f 72 72 65 63 | 74 2e 0d 0a 00 00 17 4f |..Correc|t......O|
|00000a10| 04 0d 0b 00 4e 6f 2e 20 | 20 49 74 20 6c 6f 6f 6b |....No. | It look|
|00000a20| 73 20 6c 69 6b 65 20 79 | 6f 75 20 75 73 65 64 20 |s like y|ou used |
|00000a30| 74 68 65 20 66 6f 72 6d | 75 6c 61 20 66 6f 72 20 |the form|ula for |
|00000a40| 73 69 6e 28 11 33 76 20 | 11 31 2d 20 11 33 75 11 |sin(.3v |.1- .3u.|
|00000a50| 31 29 20 69 6e 73 74 65 | 61 64 20 6f 66 20 0d 0a |1) inste|ad of ..|
|00000a60| 00 63 6f 73 28 11 33 76 | 20 11 31 2d 20 11 33 75 |.cos(.3v| .1- .3u|
|00000a70| 11 31 29 2e 20 20 63 6f | 73 28 11 33 76 20 11 31 |.1). co|s(.3v .1|
|00000a80| 2d 20 11 33 75 11 31 29 | 20 3d 20 63 6f 73 20 11 |- .3u.1)| = cos .|
|00000a90| 33 76 20 11 31 63 6f 73 | 20 11 33 75 20 11 31 2b |3v .1cos| .3u .1+|
|00000aa0| 20 73 69 6e 20 11 33 76 | 20 11 31 73 69 6e 20 11 | sin .3v| .1sin .|
|00000ab0| 33 75 11 31 2e 0d 0a 00 | 00 17 4f 08 0d 0b 00 20 |3u.1....|..O.... |
|00000ac0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ad0| 20 20 20 20 20 20 37 20 | 20 20 20 20 11 34 70 20 | 7 | .4p |
|00000ae0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000af0| 20 20 20 20 20 20 20 11 | 31 32 34 0d 0b 00 57 72 | .|124...Wr|
|00000b00| 6f 6e 67 2e 20 20 53 69 | 6e 63 65 20 73 69 6e 20 |ong. Si|nce sin |
|00000b10| 11 33 75 20 11 31 3d 20 | 11 34 32 32 20 11 31 61 |.3u .1= |.422 .1a|
|00000b20| 6e 64 20 11 34 32 20 11 | 31 3c 20 11 33 75 20 11 |nd .42 .|1< .3u .|
|00000b30| 31 3c 20 11 34 70 11 31 | 2c 20 74 68 65 6e 20 63 |1< .4p.1|, then c|
|00000b40| 6f 73 20 11 33 75 20 11 | 31 3d 20 2d 11 34 32 32 |os .3u .|1= -.422|
|00000b50| 20 11 31 61 6e 64 20 73 | 69 6e 63 65 0d 0b 00 20 | .1and s|ince... |
|00000b60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000b70| 20 20 20 20 20 32 35 20 | 20 20 20 20 32 20 20 20 | 25 | 2 |
|00000b80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000b90| 20 20 20 20 20 32 35 0d | 0a 00 20 20 20 20 20 20 | 25.|.. |
|00000ba0| 20 20 34 20 20 20 20 20 | 33 11 34 70 20 20 20 20 | 4 |3.4p |
|00000bb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000bc0| 20 20 20 20 20 11 31 33 | 0d 0b 00 63 6f 73 20 11 | .13|...cos .|
|00000bd0| 33 76 20 11 31 3d 20 11 | 34 32 20 11 31 61 6e 64 |3v .1= .|42 .1and|
|00000be0| 20 11 34 32 32 20 11 31 | 3c 20 11 33 76 20 11 31 | .422 .1|< .3v .1|
|00000bf0| 3c 20 32 11 34 70 11 31 | 2c 20 74 68 65 6e 20 73 |< 2.4p.1|, then s|
|00000c00| 69 6e 20 11 33 76 20 11 | 31 3d 20 2d 11 34 32 11 |in .3v .|1= -.42.|
|00000c10| 31 2e 20 20 54 68 65 6e | 2c 20 77 65 20 67 65 74 |1. Then|, we get|
|00000c20| 0d 0b 00 20 20 20 20 20 | 20 20 20 35 20 20 20 20 |... | 5 |
|00000c30| 20 20 32 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 2 | |
|00000c40| 20 20 20 20 20 20 20 20 | 20 20 20 20 35 0d 0a 00 | | 5...|
|00000c50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000c60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000c70| 20 20 20 20 20 20 20 20 | 20 20 31 31 37 0d 0b 00 | | 117...|
|00000c80| 63 6f 73 28 11 33 76 20 | 11 31 2d 20 11 33 75 11 |cos(.3v |.1- .3u.|
|00000c90| 31 29 20 3d 20 63 6f 73 | 20 11 33 76 20 11 31 63 |1) = cos| .3v .1c|
|00000ca0| 6f 73 20 11 33 75 20 11 | 31 2b 20 73 69 6e 20 11 |os .3u .|1+ sin .|
|00000cb0| 33 76 20 11 31 73 69 6e | 20 11 33 75 20 11 31 3d |3v .1sin| .3u .1=|
|00000cc0| 20 2d 11 34 32 32 32 11 | 31 2e 0d 0b 00 20 20 20 | -.4222.|1.... |
|00000cd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ce0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000cf0| 20 20 20 20 20 20 20 31 | 32 35 0d 0a 00 00 17 4f | 1|25.....O|
|00000d00| 03 0d 0b 00 43 6f 72 72 | 65 63 74 2e 0d 0a 00 00 |....Corr|ect.....|
|00000d10| 17 4f 04 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |.O.... | |
|00000d20| 20 20 20 20 11 34 67 32 | 32 32 32 32 32 20 20 20 | .4g2|22222 |
|00000d30| 20 20 67 32 32 32 32 32 | 32 20 20 20 20 20 67 32 | g22222|2 g2|
|00000d40| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|00000d50| 66 20 11 32 32 20 20 20 | 20 32 20 20 20 20 11 34 |f .22 | 2 .4|
|00000d60| 66 20 11 32 32 20 20 20 | 20 32 20 20 20 20 11 34 |f .22 | 2 .4|
|00000d70| 66 0d 0b 00 11 31 4e 6f | 74 20 71 75 69 74 65 2e |f....1No|t quite.|
|00000d80| 20 20 11 34 76 20 11 33 | 61 20 20 11 31 2b 20 11 | .4v .3|a .1+ .|
|00000d90| 33 62 20 20 11 31 3d 20 | 11 34 76 20 11 31 34 20 |3b .1= |.4v .14 |
|00000da0| 20 2b 20 33 20 20 3d 20 | 11 34 76 20 11 31 32 35 | + 3 = |.4v .125|
|00000db0| 20 3d 20 35 2e 0d 0a 00 | 00 17 4f 04 0d 0b 00 20 | = 5....|..O.... |
|00000dc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000dd0| 20 20 20 20 20 20 11 33 | 62 20 20 20 20 20 20 20 | .3|b |
|00000de0| 20 20 20 11 31 33 0d 0b | 00 4e 6f 74 20 71 75 69 | .13..|.Not qui|
|00000df0| 74 65 2e 20 20 11 33 43 | 20 11 31 3d 20 61 72 63 |te. .3C| .1= arc|
|00000e00| 74 61 6e 20 11 34 32 20 | 11 31 3d 20 61 72 63 74 |tan .42 |.1= arct|
|00000e10| 61 6e 20 11 34 32 20 7e | 20 11 31 30 2e 36 34 33 |an .42 ~| .10.643|
|00000e20| 35 2e 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |5.... | |
|00000e30| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 33 61 20 | | .3a |
|00000e40| 20 20 20 20 20 20 20 20 | 20 11 31 34 0d 0a 00 00 | | .14....|
|00000e50| 17 4f 05 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |.O.... | |
|00000e60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000e70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 33 | | 3|
|00000e80| 0d 0b 00 56 65 72 79 20 | 67 6f 6f 64 2e 20 20 11 |...Very |good. .|
|00000e90| 33 61 20 11 31 3d 20 34 | 2c 20 11 33 62 20 11 31 |3a .1= 4|, .3b .1|
|00000ea0| 3d 20 33 2c 20 61 6e 64 | 20 11 33 43 20 11 31 3d |= 3, and| .3C .1=|
|00000eb0| 20 61 72 63 74 61 6e 20 | 11 34 32 20 7e 20 11 31 | arctan |.42 ~ .1|
|00000ec0| 30 2e 36 34 33 35 2c 20 | 74 68 75 73 0d 0b 00 20 |0.6435, |thus... |
|00000ed0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ee0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ef0| 20 20 20 20 20 20 20 20 | 34 0d 0a 00 34 20 73 69 | |4...4 si|
|00000f00| 6e 20 35 11 34 74 20 11 | 31 2b 20 33 20 63 6f 73 |n 5.4t .|1+ 3 cos|
|00000f10| 20 35 11 34 74 20 11 31 | 3d 20 35 20 73 69 6e 20 | 5.4t .1|= 5 sin |
|00000f20| 28 35 11 34 74 20 11 31 | 2b 20 30 2e 36 34 33 35 |(5.4t .1|+ 0.6435|
|00000f30| 29 2e 0d 0a 00 00 17 4f | 06 0d 0b 00 20 20 20 20 |)......O|.... |
|00000f40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000f50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000f60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000f70| 11 34 67 32 32 32 32 32 | 32 20 20 20 20 20 67 32 |.4g22222|2 g2|
|00000f80| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|00000f90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000fa0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000fb0| 20 20 20 20 20 20 66 20 | 11 32 32 20 20 20 20 32 | f |.22 2|
|00000fc0| 20 20 20 20 11 34 66 0d | 0b 00 11 31 57 72 6f 6e | .4f.|...1Wron|
|00000fd0| 67 2e 20 20 54 68 65 72 | 65 20 61 72 65 20 61 20 |g. Ther|e are a |
|00000fe0| 63 6f 75 70 6c 65 20 6d | 69 73 74 61 6b 65 73 20 |couple m|istakes |
|00000ff0| 68 65 72 65 2e 20 20 46 | 69 72 73 74 2c 20 11 34 |here. F|irst, .4|
|00001000| 76 20 11 33 61 20 20 11 | 31 2b 20 11 33 62 20 20 |v .3a .|1+ .3b |
|00001010| 11 31 3d 20 11 34 76 20 | 11 31 32 35 20 3d 20 35 |.1= .4v |.125 = 5|
|00001020| 20 6e 6f 74 0d 0a 00 20 | 20 20 20 20 20 20 20 20 | not... | |
|00001030| 20 20 20 20 20 20 20 20 | 20 20 33 0d 0b 00 32 35 | | 3...25|
|00001040| 2c 20 61 6e 64 20 11 33 | 43 20 11 31 3d 20 61 72 |, and .3|C .1= ar|
|00001050| 63 74 61 6e 20 11 34 32 | 20 7e 20 11 31 30 2e 36 |ctan .42| ~ .10.6|
|00001060| 34 33 35 2e 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |435.... | |
|00001070| 20 20 20 20 20 20 20 20 | 20 20 34 0d 0a 00 00 17 | | 4.....|
|00001080| 4f 04 0d 0b 00 4e 6f 2e | 20 20 63 6f 73 28 61 72 |O....No.| cos(ar|
|00001090| 63 63 6f 73 20 11 33 78 | 20 11 31 2d 20 61 72 63 |ccos .3x| .1- arc|
|000010a0| 73 69 6e 20 11 33 78 11 | 31 29 20 11 34 3d 20 11 |sin .3x.|1) .4= .|
|000010b0| 31 63 6f 73 28 61 72 63 | 63 6f 73 20 11 33 78 11 |1cos(arc|cos .3x.|
|000010c0| 31 29 20 2d 20 63 6f 73 | 28 61 72 63 73 69 6e 20 |1) - cos|(arcsin |
|000010d0| 11 33 78 11 31 29 2e 20 | 20 55 73 65 0d 0a 00 74 |.3x.1). | Use...t|
|000010e0| 68 65 20 66 6f 72 6d 75 | 6c 61 20 63 6f 73 28 11 |he formu|la cos(.|
|000010f0| 33 75 20 11 31 2d 20 11 | 33 76 11 31 29 20 3d 20 |3u .1- .|3v.1) = |
|00001100| 63 6f 73 20 11 33 75 20 | 11 31 63 6f 73 20 11 33 |cos .3u |.1cos .3|
|00001110| 76 20 11 31 2b 20 73 69 | 6e 20 11 33 75 20 11 31 |v .1+ si|n .3u .1|
|00001120| 73 69 6e 20 11 33 76 11 | 31 2e 0d 0a 00 00 17 4f |sin .3v.|1......O|
|00001130| 07 0d 0b 00 56 65 72 79 | 20 67 6f 6f 64 2e 20 20 |....Very| good. |
|00001140| 0d 0a 00 63 6f 73 28 61 | 72 63 63 6f 73 20 11 33 |...cos(a|rccos .3|
|00001150| 78 20 11 31 2d 20 61 72 | 63 73 69 6e 20 11 33 78 |x .1- ar|csin .3x|
|00001160| 11 31 29 20 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |.1) ... | |
|00001170| 20 20 20 20 20 20 20 3d | 20 63 6f 73 28 61 72 63 | =| cos(arc|
|00001180| 63 6f 73 20 11 33 78 11 | 31 29 20 63 6f 73 28 61 |cos .3x.|1) cos(a|
|00001190| 72 63 73 69 6e 20 11 33 | 78 11 31 29 20 2b 20 73 |rcsin .3|x.1) + s|
|000011a0| 69 6e 28 61 72 63 63 6f | 73 20 11 33 78 11 31 29 |in(arcco|s .3x.1)|
|000011b0| 20 73 69 6e 28 61 72 63 | 73 69 6e 20 11 33 78 11 | sin(arc|sin .3x.|
|000011c0| 31 29 0d 0a 00 20 20 20 | 20 20 20 20 20 20 20 20 |1)... | |
|000011d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 34 67 | | .4g|
|000011e0| 32 32 32 32 32 20 20 20 | 20 20 67 32 32 32 32 32 |22222 | g22222|
|000011f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 67 32 32 | | g22|
|00001200| 32 32 32 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |222... | |
|00001210| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 66 20 20 | | f |
|00001220| 20 20 20 11 32 32 20 20 | 20 20 11 34 66 20 20 20 | .22 | .4f |
|00001230| 20 20 11 32 32 20 20 20 | 20 20 20 20 20 20 20 20 | .22 | |
|00001240| 20 11 34 66 20 20 20 20 | 20 11 32 32 0d 0b 00 20 | .4f | .22... |
|00001250| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00001260| 31 3d 20 11 33 78 20 11 | 34 2a 20 76 20 11 31 31 |1= .3x .|4* v .11|
|00001270| 20 2d 20 11 33 78 20 20 | 11 31 2b 20 11 34 76 20 | - .3x |.1+ .4v |
|00001280| 11 31 31 20 2d 20 11 33 | 78 20 20 11 34 2a 20 11 |.11 - .3|x .4* .|
|00001290| 33 78 20 20 11 31 3d 20 | 32 11 33 78 20 11 34 76 |3x .1= |2.3x .4v|
|000012a0| 20 11 31 31 20 2d 20 11 | 33 78 0d 0a 00 00 17 4f | .11 - .|3x.....O|
|000012b0| 04 0d 0b 00 4e 6f 2e 20 | 20 59 6f 75 20 75 73 65 |....No. | You use|
|000012c0| 64 20 74 68 65 20 77 72 | 6f 6e 67 20 66 6f 72 6d |d the wr|ong form|
|000012d0| 75 6c 61 2e 20 20 55 73 | 65 20 74 68 65 20 66 6f |ula. Us|e the fo|
|000012e0| 72 6d 75 6c 61 20 0d 0a | 00 63 6f 73 28 11 33 75 |rmula ..|.cos(.3u|
|000012f0| 20 11 31 2d 20 11 33 76 | 11 31 29 20 3d 20 63 6f | .1- .3v|.1) = co|
|00001300| 73 20 11 33 75 20 11 31 | 63 6f 73 20 11 33 76 20 |s .3u .1|cos .3v |
|00001310| 11 31 2b 20 73 69 6e 20 | 11 33 75 20 11 31 73 69 |.1+ sin |.3u .1si|
|00001320| 6e 20 11 33 76 11 31 2e | 0d 0a 00 00 17 4f 07 0d |n .3v.1.|.....O..|
|00001330| 0b 00 57 72 6f 6e 67 2e | 20 20 0d 0a 00 63 6f 73 |..Wrong.| ...cos|
|00001340| 28 61 72 63 63 6f 73 20 | 11 33 78 20 11 31 2d 20 |(arccos |.3x .1- |
|00001350| 61 72 63 73 69 6e 20 11 | 33 78 11 31 29 20 0d 0a |arcsin .|3x.1) ..|
|00001360| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00001370| 20 3d 20 63 6f 73 28 61 | 72 63 63 6f 73 20 11 33 | = cos(a|rccos .3|
|00001380| 78 11 31 29 20 63 6f 73 | 28 61 72 63 73 69 6e 20 |x.1) cos|(arcsin |
|00001390| 11 33 78 11 31 29 20 2b | 20 73 69 6e 28 61 72 63 |.3x.1) +| sin(arc|
|000013a0| 63 6f 73 20 11 33 78 11 | 31 29 20 73 69 6e 28 61 |cos .3x.|1) sin(a|
|000013b0| 72 63 73 69 6e 20 11 33 | 78 11 31 29 0d 0a 00 20 |rcsin .3|x.1)... |
|000013c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000013d0| 20 20 20 20 20 20 20 11 | 34 67 32 32 32 32 32 20 | .|4g22222 |
|000013e0| 20 20 20 20 67 32 32 32 | 32 32 20 20 20 20 20 20 | g222|22 |
|000013f0| 20 20 20 20 20 20 20 67 | 32 32 32 32 32 0d 0b 00 | g|22222...|
|00001400| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001410| 20 20 20 20 20 20 20 66 | 20 20 20 20 20 11 32 32 | f| .22|
|00001420| 20 20 20 20 11 34 66 20 | 20 20 20 20 11 32 32 20 | .4f | .22 |
|00001430| 20 20 20 20 20 20 20 20 | 20 20 20 11 34 66 20 20 | | .4f |
|00001440| 20 20 20 11 32 32 0d 0b | 00 20 20 20 20 20 20 20 | .22..|. |
|00001450| 20 20 20 20 20 20 20 20 | 20 11 31 3d 20 11 33 78 | | .1= .3x|
|00001460| 20 11 34 2a 20 76 20 11 | 31 31 20 2d 20 11 33 78 | .4* v .|11 - .3x|
|00001470| 20 20 11 31 2b 20 11 34 | 76 20 11 31 31 20 2d 20 | .1+ .4|v .11 - |
|00001480| 11 33 78 20 20 11 34 2a | 20 11 33 78 20 20 11 31 |.3x .4*| .3x .1|
|00001490| 3d 20 32 11 33 78 20 11 | 34 76 20 11 31 31 20 2d |= 2.3x .|4v .11 -|
|000014a0| 20 11 33 78 0d 0a 00 00 | 17 4f 03 0d 0b 00 47 6f | .3x....|.O....Go|
|000014b0| 6f 64 2e 20 20 54 68 69 | 73 20 69 73 20 74 68 65 |od. Thi|s is the|
|000014c0| 20 6f 6e 6c 79 20 73 6f | 6c 75 74 69 6f 6e 20 69 | only so|lution i|
|000014d0| 6e 20 74 68 65 20 69 6e | 74 65 72 76 61 6c 20 5b |n the in|terval [|
|000014e0| 30 2c 20 32 11 34 70 11 | 31 29 2e 0d 0a 00 00 17 |0, 2.4p.|1)......|
|000014f0| 4f 07 0d 0b 00 20 20 20 | 20 20 33 11 34 70 20 20 |O.... | 3.4p |
|00001500| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001510| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001520| 20 20 20 20 20 20 70 0d | 0b 00 11 31 4e 6f 2e 20 | p.|...1No. |
|00001530| 20 11 34 32 32 20 11 31 | 69 73 20 74 68 65 20 6f | .422 .1|is the o|
|00001540| 6e 6c 79 20 73 6f 6c 75 | 74 69 6f 6e 2e 20 20 57 |nly solu|tion. W|
|00001550| 65 20 63 61 6e 20 73 65 | 65 20 74 68 61 74 20 11 |e can se|e that .|
|00001560| 34 32 20 11 31 69 73 20 | 6e 6f 74 20 61 20 73 6f |42 .1is |not a so|
|00001570| 6c 75 74 69 6f 6e 20 62 | 79 20 0d 0b 00 20 20 20 |lution b|y ... |
|00001580| 20 20 20 32 20 20 20 20 | 20 20 20 20 20 20 20 20 | 2 | |
|00001590| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000015a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 32 0d 0a 00 | | 2...|
|000015b0| 63 68 65 63 6b 69 6e 67 | 20 69 74 20 69 6e 20 74 |checking| it in t|
|000015c0| 68 65 20 67 69 76 65 6e | 20 65 71 75 61 74 69 6f |he given| equatio|
|000015d0| 6e 2e 20 20 53 69 6e 63 | 65 20 74 68 65 79 20 61 |n. Sinc|e they a|
|000015e0| 72 65 20 6e 6f 74 20 69 | 6e 20 74 68 65 20 69 6e |re not i|n the in|
|000015f0| 74 65 72 76 61 6c 0d 0a | 00 20 20 20 20 20 20 20 |terval..|. |
|00001600| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001610| 20 20 20 20 20 20 20 20 | 20 20 35 11 34 70 20 20 | | 5.4p |
|00001620| 20 20 20 11 31 37 11 34 | 70 0d 0b 00 11 31 5b 30 | .17.4|p....1[0|
|00001630| 2c 20 32 11 34 70 11 31 | 29 2c 20 77 65 20 64 6f |, 2.4p.1|), we do|
|00001640| 20 6e 6f 74 20 6e 65 65 | 64 20 74 6f 20 63 68 65 | not nee|d to che|
|00001650| 63 6b 20 11 34 32 32 20 | 11 31 61 6e 64 20 11 34 |ck .422 |.1and .4|
|00001660| 32 32 11 31 2e 0d 0b 00 | 20 20 20 20 20 20 20 20 |22.1....| |
|00001670| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001680| 20 20 20 20 20 20 20 20 | 20 20 32 20 20 20 20 20 | | 2 |
|00001690| 20 32 0d 0a 00 00 17 4f | 06 0d 0b 00 20 20 20 20 | 2.....O|.... |
|000016a0| 20 33 11 34 70 20 20 20 | 20 20 20 20 20 20 20 20 | 3.4p | |
|000016b0| 20 20 20 20 20 20 20 20 | 20 70 0d 0b 00 11 31 4e | | p....1N|
|000016c0| 6f 2e 20 20 11 34 32 32 | 20 11 31 69 73 20 61 20 |o. .422| .1is a |
|000016d0| 73 6f 6c 75 74 69 6f 6e | 2c 20 62 75 74 20 11 34 |solution|, but .4|
|000016e0| 32 20 11 31 69 73 20 6e | 6f 74 20 73 69 6e 63 65 |2 .1is n|ot since|
|000016f0| 0d 0b 00 20 20 20 20 20 | 20 32 20 20 20 20 20 20 |... | 2 |
|00001700| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 32 0d | | 2.|
|00001710| 0a 00 20 20 20 20 11 34 | 70 20 20 20 70 20 20 20 |.. .4|p p |
|00001720| 20 20 20 20 20 70 20 20 | 20 70 20 20 20 20 20 11 | p | p .|
|00001730| 31 31 20 20 20 31 0d 0b | 00 63 6f 73 28 11 34 32 |11 1..|.cos(.42|
|00001740| 20 11 31 2b 20 11 34 32 | 11 31 29 20 2d 20 63 6f | .1+ .42|.1) - co|
|00001750| 73 28 11 34 32 20 11 31 | 2d 20 11 34 32 11 31 29 |s(.42 .1|- .42.1)|
|00001760| 20 3d 20 2d 11 34 32 20 | 11 31 2b 20 11 34 32 20 | = -.42 |.1+ .42 |
|00001770| 11 31 3d 20 30 20 11 34 | 3d 20 11 31 31 2e 0d 0b |.1= 0 .4|= .11...|
|00001780| 00 20 20 20 20 32 20 20 | 20 36 20 20 20 20 20 20 |. 2 | 6 |
|00001790| 20 20 32 20 20 20 36 20 | 20 20 20 20 32 20 20 20 | 2 6 | 2 |
|000017a0| 32 0d 0a 00 00 17 4f 04 | 0d 0b 00 20 20 20 20 20 |2.....O.|... |
|000017b0| 20 20 20 11 34 70 20 20 | 20 20 20 20 20 20 20 20 | .4p | |
|000017c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000017d0| 20 20 20 70 20 20 20 70 | 20 20 20 20 20 20 20 20 | p p| |
|000017e0| 70 20 20 20 70 20 20 20 | 20 20 11 31 31 20 20 20 |p p | .11 |
|000017f0| 31 0d 0b 00 57 72 6f 6e | 67 2e 20 20 11 34 32 20 |1...Wron|g. .42 |
|00001800| 11 31 69 73 20 6e 6f 74 | 20 61 20 73 6f 6c 75 74 |.1is not| a solut|
|00001810| 69 6f 6e 20 73 69 6e 63 | 65 20 63 6f 73 28 11 34 |ion sinc|e cos(.4|
|00001820| 32 20 11 31 2b 20 11 34 | 32 11 31 29 20 2d 20 63 |2 .1+ .4|2.1) - c|
|00001830| 6f 73 28 11 34 32 20 11 | 31 2d 20 11 34 32 11 31 |os(.42 .|1- .42.1|
|00001840| 29 20 3d 20 2d 11 34 32 | 20 11 31 2b 20 11 34 32 |) = -.42| .1+ .42|
|00001850| 20 11 31 3d 20 30 20 11 | 34 3d 20 11 31 31 2e 0d | .1= 0 .|4= .11..|
|00001860| 0b 00 20 20 20 20 20 20 | 20 20 32 20 20 20 20 20 |.. | 2 |
|00001870| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001880| 20 20 20 20 20 20 20 20 | 32 20 20 20 36 20 20 20 | |2 6 |
|00001890| 20 20 20 20 20 32 20 20 | 20 36 20 20 20 20 20 32 | 2 | 6 2|
|000018a0| 20 20 20 32 0d 0a 00 00 | 17 4f 06 20 20 20 20 20 | 2....|.O. |
|000018b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000018c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000018d0| 20 20 11 34 6f 20 20 20 | 20 20 20 6f 20 20 20 20 | .4o | o |
|000018e0| 20 6f 0d 0b 00 11 31 57 | 72 6f 6e 67 2e 20 20 54 | o....1W|rong. T|
|000018f0| 68 69 73 20 6f 6e 65 20 | 69 73 20 63 6f 72 72 65 |his one |is corre|
|00001900| 63 74 2e 20 20 53 69 6e | 63 65 20 32 38 35 20 20 |ct. Sin|ce 285 |
|00001910| 3d 20 33 31 35 20 20 2d | 20 33 30 20 20 61 6e 64 |= 315 -| 30 and|
|00001920| 20 0d 0a 00 0d 0b 00 73 | 69 6e 28 11 33 75 20 11 | ......s|in(.3u .|
|00001930| 31 2d 20 11 33 76 11 31 | 29 20 3d 20 73 69 6e 20 |1- .3v.1|) = sin |
|00001940| 11 33 75 20 11 31 63 6f | 73 20 11 33 76 20 11 31 |.3u .1co|s .3v .1|
|00001950| 2d 20 63 6f 73 20 11 33 | 75 20 11 31 73 69 6e 20 |- cos .3|u .1sin |
|00001960| 11 33 76 11 31 2c 20 74 | 68 65 6e 20 77 65 20 6b |.3v.1, t|hen we k|
|00001970| 6e 6f 77 20 0d 0a 00 20 | 20 20 20 20 20 20 11 34 |now ... | .4|
|00001980| 6f 20 20 20 20 20 20 20 | 20 20 20 6f 20 20 20 20 |o | o |
|00001990| 20 20 20 6f 20 20 20 20 | 20 20 20 20 20 20 6f 20 | o | o |
|000019a0| 20 20 20 20 20 20 6f 20 | 20 20 20 11 31 31 20 20 | o | .11 |
|000019b0| 11 34 44 32 20 20 20 20 | 44 32 0d 0b 00 11 31 73 |.4D2 |D2....1s|
|000019c0| 69 6e 20 32 38 35 20 20 | 3d 20 73 69 6e 20 33 31 |in 285 |= sin 31|
|000019d0| 35 20 20 63 6f 73 20 33 | 30 20 20 2d 20 63 6f 73 |5 cos 3|0 - cos|
|000019e0| 20 33 31 35 20 20 73 69 | 6e 20 33 30 20 20 3d 20 | 315 si|n 30 = |
|000019f0| 2d 11 34 32 11 31 28 11 | 34 53 20 11 31 36 20 2b |-.42.1(.|4S .16 +|
|00001a00| 20 11 34 53 20 11 31 32 | 29 2e 0d 0b 00 20 20 20 | .4S .12|).... |
|00001a10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001a20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001a30| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 34 | | 4|
|00001a40| 0d 0a 00 00 17 4f 06 20 | 20 20 20 20 20 20 20 20 |.....O. | |
|00001a50| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 34 6f 20 | | .4o |
|00001a60| 20 20 20 20 20 6f 20 20 | 20 20 20 6f 0d 0b 00 11 | o | o....|
|00001a70| 31 56 65 72 79 20 67 6f | 6f 64 2e 20 20 53 69 6e |1Very go|od. Sin|
|00001a80| 63 65 20 32 38 35 20 20 | 3d 20 33 31 35 20 20 2d |ce 285 |= 315 -|
|00001a90| 20 33 30 20 20 61 6e 64 | 20 0d 0a 00 0d 0b 00 63 | 30 and| ......c|
|00001aa0| 6f 73 20 28 11 33 75 20 | 11 31 2d 20 11 33 76 11 |os (.3u |.1- .3v.|
|00001ab0| 31 29 20 3d 20 63 6f 73 | 20 11 33 75 20 11 31 63 |1) = cos| .3u .1c|
|00001ac0| 6f 73 20 11 33 76 20 11 | 31 2b 20 73 69 6e 20 11 |os .3v .|1+ sin .|
|00001ad0| 33 75 20 11 31 73 69 6e | 20 11 33 76 11 31 2c 20 |3u .1sin| .3v.1, |
|00001ae0| 74 68 65 6e 20 77 65 20 | 6b 6e 6f 77 0d 0a 00 20 |then we |know... |
|00001af0| 20 20 20 20 20 20 11 34 | 6f 20 20 20 20 20 20 20 | .4|o |
|00001b00| 20 20 20 6f 20 20 20 20 | 20 20 20 6f 20 20 20 20 | o | o |
|00001b10| 20 20 20 20 20 20 6f 20 | 20 20 20 20 20 20 6f 20 | o | o |
|00001b20| 20 11 31 31 20 20 11 34 | 44 32 20 20 20 20 44 32 | .11 .4|D2 D2|
|00001b30| 0d 0b 00 11 31 63 6f 73 | 20 32 38 35 20 20 3d 20 |....1cos| 285 = |
|00001b40| 63 6f 73 20 33 31 35 20 | 20 63 6f 73 20 33 30 20 |cos 315 | cos 30 |
|00001b50| 20 2b 20 73 69 6e 20 33 | 31 35 20 20 73 69 6e 20 | + sin 3|15 sin |
|00001b60| 33 30 20 3d 20 11 34 32 | 11 31 28 11 34 53 20 11 |30 = .42|.1(.4S .|
|00001b70| 31 36 20 2d 20 11 34 53 | 20 11 31 32 29 2e 0d 0b |16 - .4S| .12)...|
|00001b80| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00001b90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001bb0| 20 34 0d 0a 00 00 17 4f | 06 20 20 20 20 20 20 20 | 4.....O|. |
|00001bc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001bd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001be0| 20 20 20 20 20 20 20 20 | 20 20 20 74 61 6e 20 11 | | tan .|
|00001bf0| 33 75 20 11 31 2d 20 74 | 61 6e 20 11 33 76 0d 0b |3u .1- t|an .3v..|
|00001c00| 00 11 31 53 6f 72 72 79 | 2c 20 74 68 69 73 20 6f |..1Sorry|, this o|
|00001c10| 6e 65 20 69 73 20 63 6f | 72 72 65 63 74 2e 20 20 |ne is co|rrect. |
|00001c20| 53 69 6e 63 65 20 74 61 | 6e 20 28 11 33 75 20 11 |Since ta|n (.3u .|
|00001c30| 31 2d 20 11 33 76 11 31 | 29 20 3d 20 11 34 32 32 |1- .3v.1|) = .422|
|00001c40| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 0d 0b 00 |22222222|22222...|
|00001c50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001c60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001c70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001c80| 20 11 31 31 20 2b 20 74 | 61 6e 20 11 33 75 20 11 | .11 + t|an .3u .|
|00001c90| 31 74 61 6e 20 11 33 76 | 0d 0a 00 20 20 20 20 20 |1tan .3v|... |
|00001ca0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001cb0| 20 20 20 20 11 34 6f 20 | 20 20 20 20 20 20 20 20 | .4o | |
|00001cc0| 6f 20 20 20 20 20 20 20 | 20 20 20 20 20 6f 20 20 |o | o |
|00001cd0| 20 20 20 20 20 20 20 20 | 6f 0d 0b 00 20 20 20 20 | |o... |
|00001ce0| 20 20 20 20 20 20 20 20 | 20 6f 20 20 20 20 11 31 | | o .1|
|00001cf0| 74 61 6e 20 33 31 35 20 | 20 2d 20 74 61 6e 20 33 |tan 315 | - tan 3|
|00001d00| 30 20 20 20 20 20 20 74 | 61 6e 28 2d 34 35 20 29 |0 t|an(-45 )|
|00001d10| 20 2d 20 74 61 6e 20 33 | 30 20 20 20 20 20 20 20 | - tan 3|0 |
|00001d20| 20 20 20 20 11 34 44 32 | 0d 0b 00 11 31 74 68 65 | .4D2|....1the|
|00001d30| 6e 2c 20 74 61 6e 20 32 | 38 35 20 20 3d 20 11 34 |n, tan 2|85 = .4|
|00001d40| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|00001d50| 32 32 32 32 20 11 31 3d | 20 11 34 32 32 32 32 32 |2222 .1=| .422222|
|00001d60| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|00001d70| 20 11 31 3d 20 2d 32 20 | 2d 20 11 34 53 20 11 31 | .1= -2 |- .4S .1|
|00001d80| 33 2e 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |3.... | |
|00001d90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001da0| 20 11 34 6f 20 20 20 20 | 20 20 20 6f 20 20 20 20 | .4o | o |
|00001db0| 20 20 20 20 20 20 20 20 | 20 20 6f 20 20 20 20 20 | | o |
|00001dc0| 20 20 20 6f 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | o... | |
|00001dd0| 20 20 20 20 20 20 20 20 | 11 31 31 20 2b 20 74 61 | |.11 + ta|
|00001de0| 6e 20 33 31 35 20 20 74 | 61 6e 20 33 30 20 20 20 |n 315 t|an 30 |
|00001df0| 20 31 20 2b 20 74 61 6e | 28 2d 34 35 20 29 20 74 | 1 + tan|(-45 ) t|
|00001e00| 61 6e 20 33 30 0d 0a 00 | 00 17 4f 03 0d 0b 00 53 |an 30...|..O....S|
|00001e10| 6f 72 72 79 2c 20 6e 6f | 74 20 61 6c 6c 20 6f 66 |orry, no|t all of|
|00001e20| 20 74 68 65 73 65 20 61 | 6e 73 77 65 72 73 20 61 | these a|nswers a|
|00001e30| 72 65 20 63 6f 72 72 65 | 63 74 2e 20 20 50 6c 65 |re corre|ct. Ple|
|00001e40| 61 73 65 20 74 72 79 20 | 61 67 61 69 6e 2e 0d 0a |ase try |again...|
|00001e50| 00 53 65 63 74 69 6f 6e | 20 37 2e 34 20 20 53 75 |.Section| 7.4 Su|
|00001e60| 6d 20 61 6e 64 20 44 69 | 66 66 65 72 65 6e 63 65 |m and Di|fference|
|00001e70| 20 46 6f 72 6d 75 6c 61 | 73 0d 0a 00 0d 0a 00 0d | Formula|s.......|
|00001e80| 0b 00 20 20 20 20 0e 78 | 37 2d 34 2d 31 0e 54 75 |.. .x|7-4-1.Tu|
|00001e90| 74 6f 72 69 61 6c 20 45 | 78 65 72 63 69 73 65 20 |torial E|xercise |
|00001ea0| 20 31 0f 0d 0a 00 0d 0b | 00 20 20 20 20 0e 78 37 | 1......|. .x7|
|00001eb0| 2d 34 2d 32 0e 54 75 74 | 6f 72 69 61 6c 20 45 78 |-4-2.Tut|orial Ex|
|00001ec0| 65 72 63 69 73 65 20 20 | 32 0f 20 20 20 20 0e 78 |ercise |2. .x|
|00001ed0| 37 2d 34 2d 33 0e 54 75 | 74 6f 72 69 61 6c 20 45 |7-4-3.Tu|torial E|
|00001ee0| 78 65 72 63 69 73 65 20 | 33 0f 20 20 20 20 0e 78 |xercise |3. .x|
|00001ef0| 37 2d 34 2d 34 0e 54 75 | 74 6f 72 69 61 6c 20 45 |7-4-4.Tu|torial E|
|00001f00| 78 65 72 63 69 73 65 20 | 20 34 0f 0d 0a 00 0d 0b |xercise | 4......|
|00001f10| 00 20 20 20 20 0e 78 37 | 2d 34 2d 35 0e 54 75 74 |. .x7|-4-5.Tut|
|00001f20| 6f 72 69 61 6c 20 45 78 | 65 72 63 69 73 65 20 20 |orial Ex|ercise |
|00001f30| 35 0f 0d 0a 00 0d 0b 00 | 20 20 20 20 0e 78 37 2d |5.......| .x7-|
|00001f40| 34 2d 36 0e 54 75 74 6f | 72 69 61 6c 20 45 78 65 |4-6.Tuto|rial Exe|
|00001f50| 72 63 69 73 65 20 20 36 | 0f 0d 0a 00 0d 0b 00 20 |rcise 6|....... |
|00001f60| 20 20 20 0e 78 37 2d 34 | 2d 37 0e 54 75 74 6f 72 | .x7-4|-7.Tutor|
|00001f70| 69 61 6c 20 45 78 65 72 | 63 69 73 65 20 20 37 0f |ial Exer|cise 7.|
|00001f80| 0d 0a 00 0d 0b 00 20 20 | 20 20 0e 78 37 2d 34 2d |...... | .x7-4-|
|00001f90| 38 0e 54 75 74 6f 72 69 | 61 6c 20 45 78 65 72 63 |8.Tutori|al Exerc|
|00001fa0| 69 73 65 20 20 38 0f 0d | 0a 00 0d 0b 00 20 20 20 |ise 8..|..... |
|00001fb0| 20 0e 78 37 2d 34 2d 39 | 0e 54 75 74 6f 72 69 61 | .x7-4-9|.Tutoria|
|00001fc0| 6c 20 45 78 65 72 63 69 | 73 65 20 20 39 0f 0d 0a |l Exerci|se 9...|
|00001fd0| 00 53 65 63 74 69 6f 6e | 20 37 2e 34 20 20 53 75 |.Section| 7.4 Su|
|00001fe0| 6d 20 61 6e 64 20 44 69 | 66 66 65 72 65 6e 63 65 |m and Di|fference|
|00001ff0| 20 46 6f 72 6d 75 6c 61 | 73 0d 0b 00 20 31 2e 20 | Formula|s... 1. |
|00002000| 20 44 65 74 65 72 6d 69 | 6e 65 20 77 68 69 63 68 | Determi|ne which|
|00002010| 20 65 78 61 63 74 20 76 | 61 6c 75 65 20 6f 66 20 | exact v|alue of |
|00002020| 74 68 65 20 67 69 76 65 | 6e 20 74 72 69 67 6f 6e |the give|n trigon|
|00002030| 6f 6d 65 74 72 69 63 20 | 66 75 6e 63 74 69 6f 6e |ometric |function|
|00002040| 20 69 73 0d 0a 00 20 20 | 20 20 20 20 20 20 20 20 | is... | |
|00002050| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002060| 20 20 20 20 20 20 11 34 | 6f 20 20 20 20 20 20 6f | .4|o o|
|00002070| 20 20 20 20 20 6f 0d 0b | 00 20 20 20 20 20 11 31 | o..|. .1|
|00002080| 69 6e 63 6f 72 72 65 63 | 74 20 66 6f 72 20 74 68 |incorrec|t for th|
|00002090| 65 20 61 6e 67 6c 65 20 | 32 38 35 20 20 3d 20 33 |e angle |285 = 3|
|000020a0| 31 35 20 20 2d 20 33 30 | 20 2e 0d 0a 00 0d 0a 00 |15 - 30| .......|
|000020b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000020c0| 11 34 6f 20 20 20 20 11 | 31 31 20 20 11 34 44 32 |.4o .|11 .4D2|
|000020d0| 20 20 20 20 44 32 0d 0b | 00 20 20 20 20 20 11 31 | D2..|. .1|
|000020e0| 0e 61 38 2d 34 2d 35 61 | 0e 28 61 29 0f 20 73 69 |.a8-4-5a|.(a). si|
|000020f0| 6e 20 32 38 35 20 20 3d | 20 2d 11 34 32 11 31 28 |n 285 =| -.42.1(|
|00002100| 11 34 53 20 11 31 36 20 | 2b 20 11 34 53 20 11 31 |.4S .16 |+ .4S .1|
|00002110| 32 29 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |2)... | |
|00002120| 20 20 20 20 20 20 20 20 | 20 20 34 0d 0a 00 0d 0b | | 4.....|
|00002130| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00002140| 20 11 34 6f 20 20 20 11 | 31 31 20 20 11 34 44 32 | .4o .|11 .4D2|
|00002150| 20 20 20 20 44 32 0d 0b | 00 20 20 20 20 20 11 31 | D2..|. .1|
|00002160| 0e 61 38 2d 34 2d 35 62 | 0e 28 62 29 0f 20 63 6f |.a8-4-5b|.(b). co|
|00002170| 73 20 32 38 35 20 20 3d | 20 11 34 32 11 31 28 11 |s 285 =| .42.1(.|
|00002180| 34 53 20 11 31 36 20 2b | 20 11 34 53 20 11 31 32 |4S .16 +| .4S .12|
|00002190| 29 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |)... | |
|000021a0| 20 20 20 20 20 20 20 20 | 34 0d 0a 00 0d 0b 00 20 | |4...... |
|000021b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000021c0| 20 20 20 20 20 20 20 20 | 20 11 34 44 32 0d 0b 00 | | .4D2...|
|000021d0| 20 20 20 20 20 11 31 0e | 61 38 2d 34 2d 35 63 0e | .1.|a8-4-5c.|
|000021e0| 28 63 29 0f 20 74 61 6e | 20 32 38 35 20 20 3d 20 |(c). tan| 285 = |
|000021f0| 2d 32 20 2d 20 11 34 53 | 20 11 31 33 0d 0a 00 0d |-2 - .4S| .13....|
|00002200| 0a 00 0d 0b 00 20 20 20 | 20 20 0e 61 38 2d 34 2d |..... | .a8-4-|
|00002210| 35 64 0e 28 64 29 0f 20 | 41 6c 6c 20 6f 66 20 74 |5d.(d). |All of t|
|00002220| 68 65 73 65 20 61 72 65 | 20 63 6f 72 72 65 63 74 |hese are| correct|
|00002230| 0d 0a 00 0d 0a 00 59 6f | 75 20 6d 61 79 20 77 61 |......Yo|u may wa|
|00002240| 6e 74 20 74 6f 20 72 65 | 76 69 65 77 20 10 61 37 |nt to re|view .a7|
|00002250| 2d 34 2d 32 0e 65 37 2d | 34 2d 31 0e 47 75 69 64 |-4-2.e7-|4-1.Guid|
|00002260| 65 64 20 45 78 61 6d 70 | 6c 65 20 31 2e 0f 0d 0a |ed Examp|le 1....|
|00002270| 00 53 65 63 74 69 6f 6e | 20 37 2e 34 20 20 53 75 |.Section| 7.4 Su|
|00002280| 6d 20 61 6e 64 20 44 69 | 66 66 65 72 65 6e 63 65 |m and Di|fference|
|00002290| 20 46 6f 72 6d 75 6c 61 | 73 0d 0b 00 20 20 20 20 | Formula|s... |
|000022a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000022b0| 11 34 6f 20 20 20 20 20 | 20 20 6f 20 20 20 20 20 |.4o | o |
|000022c0| 20 20 20 20 6f 20 20 20 | 20 20 20 20 6f 0d 0b 00 | o | o...|
|000022d0| 20 11 31 32 2e 20 20 53 | 69 6d 70 6c 69 66 79 20 | .12. S|implify |
|000022e0| 63 6f 73 20 35 30 20 20 | 63 6f 73 20 32 35 20 20 |cos 50 |cos 25 |
|000022f0| 2d 20 73 69 6e 20 35 30 | 20 20 73 69 6e 20 32 35 |- sin 50| sin 25|
|00002300| 20 2e 0d 0a 00 0d 0a 00 | 20 20 20 20 20 20 20 20 | .......| |
|00002310| 20 20 20 20 20 20 20 11 | 34 6f 20 20 20 20 20 20 | .|4o |
|00002320| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002330| 20 20 20 20 20 20 20 20 | 20 20 6f 0d 0b 00 20 20 | | o... |
|00002340| 20 20 20 11 31 0e 61 38 | 2d 34 2d 31 31 61 0e 28 | .1.a8|-4-11a.(|
|00002350| 61 29 0f 20 63 6f 73 20 | 32 35 20 20 20 20 20 20 |a). cos |25 |
|00002360| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002370| 20 0e 61 38 2d 34 2d 31 | 31 61 0e 28 62 29 0f 20 | .a8-4-1|1a.(b). |
|00002380| 73 69 6e 20 32 35 0d 0a | 00 0d 0b 00 20 20 20 20 |sin 25..|.... |
|00002390| 20 20 20 20 20 20 20 20 | 20 20 20 11 34 6f 20 20 | | .4o |
|000023a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000023b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 6f 0d | | o.|
|000023c0| 0b 00 20 20 20 20 20 11 | 31 0e 61 38 2d 34 2d 31 |.. .|1.a8-4-1|
|000023d0| 31 63 0e 28 63 29 0f 20 | 63 6f 73 20 37 35 20 20 |1c.(c). |cos 75 |
|000023e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000023f0| 20 20 20 20 20 0e 61 38 | 2d 34 2d 31 31 61 0e 28 | .a8|-4-11a.(|
|00002400| 64 29 0f 20 73 69 6e 20 | 37 35 0d 0a 00 0d 0a 00 |d). sin |75......|
|00002410| 59 6f 75 20 6d 61 79 20 | 77 61 6e 74 20 74 6f 20 |You may |want to |
|00002420| 72 65 76 69 65 77 20 10 | 61 37 2d 34 2d 32 0e 65 |review .|a7-4-2.e|
|00002430| 37 2d 34 2d 32 0e 47 75 | 69 64 65 64 20 45 78 61 |7-4-2.Gu|ided Exa|
|00002440| 6d 70 6c 65 20 32 2e 0f | 0d 0a 00 53 65 63 74 69 |mple 2..|...Secti|
|00002450| 6f 6e 20 37 2e 34 20 20 | 53 75 6d 20 61 6e 64 20 |on 7.4 |Sum and |
|00002460| 44 69 66 66 65 72 65 6e | 63 65 20 46 6f 72 6d 75 |Differen|ce Formu|
|00002470| 6c 61 73 0d 0b 00 20 33 | 2e 20 20 53 69 6d 70 6c |las... 3|. Simpl|
|00002480| 69 66 79 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |ify... | |
|00002490| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 34 6f 20 | | .4o |
|000024a0| 20 20 20 20 20 20 20 20 | 6f 0d 0b 00 20 20 20 20 | |o... |
|000024b0| 20 20 20 20 20 20 20 20 | 20 20 20 11 31 74 61 6e | | .1tan|
|000024c0| 20 32 33 35 20 20 2d 20 | 74 61 6e 20 36 38 0d 0b | 235 - |tan 68..|
|000024d0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |. | .|
|000024e0| 34 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |42222222|22222222|
|000024f0| 32 32 32 32 32 11 31 2e | 0d 0b 00 20 20 20 20 20 |22222.1.|... |
|00002500| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002510| 20 20 20 20 11 34 6f 20 | 20 20 20 20 20 20 6f 0d | .4o | o.|
|00002520| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00002530| 11 31 31 20 2b 20 74 61 | 6e 20 32 33 35 20 20 74 |.11 + ta|n 235 t|
|00002540| 61 6e 20 36 38 0d 0a 00 | 0d 0a 00 20 20 20 20 20 |an 68...|... |
|00002550| 20 20 20 20 20 20 20 20 | 20 20 20 11 34 6f 20 20 | | .4o |
|00002560| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002570| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 6f 0d | | o.|
|00002580| 0b 00 20 20 20 20 20 11 | 31 0e 61 38 2d 34 2d 31 |.. .|1.a8-4-1|
|00002590| 35 61 0e 28 61 29 0f 20 | 74 61 6e 20 33 30 33 20 |5a.(a). |tan 303 |
|000025a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000025b0| 20 20 20 20 20 0e 61 38 | 2d 34 2d 31 35 62 0e 28 | .a8|-4-15b.(|
|000025c0| 62 29 0f 20 74 61 6e 20 | 31 36 37 0d 0a 00 0d 0b |b). tan |167.....|
|000025d0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000025e0| 20 11 34 6f 0d 0b 00 20 | 20 20 20 20 11 31 0e 61 | .4o... | .1.a|
|000025f0| 38 2d 34 2d 31 35 63 0e | 28 63 29 0f 20 74 61 6e |8-4-15c.|(c). tan|
|00002600| 20 32 33 35 20 20 20 20 | 20 20 20 20 20 20 20 20 | 235 | |
|00002610| 20 20 20 20 20 20 20 20 | 20 20 0e 61 38 2d 34 2d | | .a8-4-|
|00002620| 31 35 64 0e 28 64 29 0f | 20 43 61 6e 6e 6f 74 20 |15d.(d).| Cannot |
|00002630| 62 65 20 73 69 6d 70 6c | 69 66 69 65 64 0d 0a 00 |be simpl|ified...|
|00002640| 0d 0a 00 59 6f 75 20 6d | 61 79 20 77 61 6e 74 20 |...You m|ay want |
|00002650| 74 6f 20 72 65 76 69 65 | 77 20 10 61 37 2d 34 2d |to revie|w .a7-4-|
|00002660| 32 0e 65 37 2d 34 2d 32 | 0e 47 75 69 64 65 64 20 |2.e7-4-2|.Guided |
|00002670| 45 78 61 6d 70 6c 65 20 | 32 2e 0f 0d 0a 00 53 65 |Example |2.....Se|
|00002680| 63 74 69 6f 6e 20 37 2e | 34 20 20 53 75 6d 20 61 |ction 7.|4 Sum a|
|00002690| 6e 64 20 44 69 66 66 65 | 72 65 6e 63 65 20 46 6f |nd Diffe|rence Fo|
|000026a0| 72 6d 75 6c 61 73 0d 0b | 00 20 34 2e 20 20 53 69 |rmulas..|. 4. Si|
|000026b0| 6d 70 6c 69 66 79 0d 0a | 00 20 20 20 20 20 20 20 |mplify..|. |
|000026c0| 20 20 20 20 20 20 20 20 | 74 61 6e 20 34 11 33 78 | |tan 4.3x|
|000026d0| 20 11 31 2b 20 74 61 6e | 20 32 11 33 78 0d 0b 00 | .1+ tan| 2.3x...|
|000026e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 34 | | .4|
|000026f0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|00002700| 32 11 31 2e 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |2.1.... | |
|00002710| 20 20 20 20 20 31 20 2d | 20 74 61 6e 20 34 11 33 | 1 -| tan 4.3|
|00002720| 78 20 11 31 74 61 6e 20 | 32 11 33 78 0d 0a 00 0d |x .1tan |2.3x....|
|00002730| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00002740| 20 11 32 32 0d 0b 00 20 | 20 20 20 20 11 31 0e 61 | .22... | .1.a|
|00002750| 38 2d 34 2d 31 39 61 0e | 28 61 29 0f 20 74 61 6e |8-4-19a.|(a). tan|
|00002760| 20 38 11 33 78 20 20 20 | 20 20 20 20 20 20 20 20 | 8.3x | |
|00002770| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 31 0e 61 | | .1.a|
|00002780| 38 2d 34 2d 31 39 62 0e | 28 62 29 0f 20 74 61 6e |8-4-19b.|(b). tan|
|00002790| 20 36 11 33 78 0d 0a 00 | 0d 0b 00 20 20 20 20 20 | 6.3x...|... |
|000027a0| 11 31 0e 61 38 2d 34 2d | 31 39 63 0e 28 63 29 0f |.1.a8-4-|19c.(c).|
|000027b0| 20 74 61 6e 20 32 11 33 | 78 20 20 20 20 20 20 20 | tan 2.3|x |
|000027c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000027d0| 11 31 0e 61 38 2d 34 2d | 31 39 64 0e 28 64 29 0f |.1.a8-4-|19d.(d).|
|000027e0| 20 43 61 6e 6e 6f 74 20 | 62 65 20 73 69 6d 70 6c | Cannot |be simpl|
|000027f0| 69 66 69 65 64 0d 0a 00 | 0d 0a 00 59 6f 75 20 6d |ified...|...You m|
|00002800| 61 79 20 77 61 6e 74 20 | 74 6f 20 72 65 76 69 65 |ay want |to revie|
|00002810| 77 20 10 61 37 2d 34 2d | 32 0e 65 37 2d 34 2d 32 |w .a7-4-|2.e7-4-2|
|00002820| 0e 47 75 69 64 65 64 20 | 45 78 61 6d 70 6c 65 20 |.Guided |Example |
|00002830| 32 2e 0f 0d 0a 00 53 65 | 63 74 69 6f 6e 20 37 2e |2.....Se|ction 7.|
|00002840| 34 20 20 53 75 6d 20 61 | 6e 64 20 44 69 66 66 65 |4 Sum a|nd Diffe|
|00002850| 72 65 6e 63 65 20 46 6f | 72 6d 75 6c 61 73 0d 0b |rence Fo|rmulas..|
|00002860| 00 20 35 2e 20 20 57 72 | 69 74 65 20 63 6f 73 28 |. 5. Wr|ite cos(|
|00002870| 61 72 63 63 6f 73 20 11 | 33 78 20 11 31 2d 20 61 |arccos .|3x .1- a|
|00002880| 72 63 73 69 6e 20 11 33 | 78 11 31 29 20 61 73 20 |rcsin .3|x.1) as |
|00002890| 61 6e 20 61 6c 67 65 62 | 72 61 69 63 20 65 78 70 |an algeb|raic exp|
|000028a0| 72 65 73 73 69 6f 6e 20 | 69 6e 20 11 33 78 11 31 |ression |in .3x.1|
|000028b0| 2e 0d 0a 00 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |....... | |
|000028c0| 20 20 20 20 20 20 11 34 | 67 32 32 32 32 32 20 20 | .4|g22222 |
|000028d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000028e0| 20 20 20 20 20 20 20 20 | 67 32 32 32 32 32 0d 0b | |g22222..|
|000028f0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 66 |. | f|
|00002900| 20 20 20 20 20 11 32 32 | 20 20 20 20 20 20 20 20 | .22| |
|00002910| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002920| 20 11 34 66 20 20 20 20 | 20 11 32 32 0d 0b 00 20 | .4f | .22... |
|00002930| 20 20 20 20 11 31 0e 61 | 38 2d 34 2d 35 33 61 0e | .1.a|8-4-53a.|
|00002940| 28 61 29 0f 20 11 33 78 | 20 11 31 2d 20 11 34 76 |(a). .3x| .1- .4v|
|00002950| 20 11 31 31 20 2d 20 11 | 33 78 20 20 20 20 20 20 | .11 - .|3x |
|00002960| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 31 0e 61 | | .1.a|
|00002970| 38 2d 34 2d 35 33 62 0e | 28 62 29 0f 20 32 11 33 |8-4-53b.|(b). 2.3|
|00002980| 78 20 11 34 76 20 11 31 | 31 20 2d 20 11 33 78 0d |x .4v .1|1 - .3x.|
|00002990| 0a 00 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |..... | |
|000029a0| 11 32 32 0d 0b 00 20 20 | 20 20 20 11 31 0e 61 38 |.22... | .1.a8|
|000029b0| 2d 34 2d 35 33 63 0e 28 | 63 29 0f 20 32 11 33 78 |-4-53c.(|c). 2.3x|
|000029c0| 20 20 11 31 2d 20 31 20 | 20 20 20 20 20 20 20 20 | .1- 1 | |
|000029d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 0e 61 38 | | .a8|
|000029e0| 2d 34 2d 35 33 64 0e 28 | 64 29 0f 20 31 0d 0a 00 |-4-53d.(|d). 1...|
|000029f0| 0d 0a 00 59 6f 75 20 6d | 61 79 20 77 61 6e 74 20 |...You m|ay want |
|00002a00| 74 6f 20 72 65 76 69 65 | 77 20 10 61 37 2d 34 2d |to revie|w .a7-4-|
|00002a10| 32 0e 65 37 2d 34 2d 33 | 0e 47 75 69 64 65 64 20 |2.e7-4-3|.Guided |
|00002a20| 45 78 61 6d 70 6c 65 20 | 33 2e 0f 0d 0a 00 53 65 |Example |3.....Se|
|00002a30| 63 74 69 6f 6e 20 37 2e | 34 20 20 53 75 6d 20 61 |ction 7.|4 Sum a|
|00002a40| 6e 64 20 44 69 66 66 65 | 72 65 6e 63 65 20 46 6f |nd Diffe|rence Fo|
|00002a50| 72 6d 75 6c 61 73 0d 0b | 00 20 20 20 20 20 20 20 |rmulas..|. |
|00002a60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002a70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002a80| 20 20 20 20 20 20 11 34 | 67 32 32 32 32 32 32 0d | .4|g222222.|
|00002a90| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00002aa0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002ab0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 66 20 | | f |
|00002ac0| 11 32 32 20 20 20 20 32 | 0d 0b 00 20 11 31 36 2e |.22 2|... .16.|
|00002ad0| 20 20 57 72 69 74 65 20 | 34 20 73 69 6e 20 35 11 | Write |4 sin 5.|
|00002ae0| 34 74 20 11 31 2b 20 33 | 20 63 6f 73 20 35 11 34 |4t .1+ 3| cos 5.4|
|00002af0| 74 20 11 31 69 6e 20 74 | 68 65 20 66 6f 72 6d 20 |t .1in t|he form |
|00002b00| 11 34 76 20 11 33 61 20 | 20 11 31 2b 20 11 33 62 |.4v .3a | .1+ .3b|
|00002b10| 20 20 11 31 73 69 6e 28 | 11 34 62 74 20 11 31 2b | .1sin(|.4bt .1+|
|00002b20| 20 11 33 43 11 31 29 20 | 62 79 0d 0a 00 20 20 20 | .3C.1) |by... |
|00002b30| 20 20 75 73 69 6e 67 20 | 74 68 65 20 66 6f 6c 6c | using |the foll|
|00002b40| 6f 77 69 6e 67 20 66 6f | 72 6d 75 6c 61 2e 0d 0a |owing fo|rmula...|
|00002b50| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00002b60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 34 | | .4|
|00002b70| 67 32 32 32 32 32 32 0d | 0b 00 20 20 20 20 20 20 |g222222.|.. |
|00002b80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002b90| 20 20 20 20 20 20 66 20 | 11 32 32 20 20 20 20 32 | f |.22 2|
|00002ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002bb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00002bc0| 33 62 0d 0b 00 20 20 20 | 20 20 61 20 11 31 73 69 |3b... | a .1si|
|00002bd0| 6e 20 11 34 62 74 20 11 | 31 2b 20 11 33 62 20 11 |n .4bt .|1+ .3b .|
|00002be0| 31 63 6f 73 20 11 34 62 | 74 20 11 31 3d 20 11 34 |1cos .4b|t .1= .4|
|00002bf0| 76 20 11 33 61 20 20 11 | 31 2b 20 11 33 62 20 20 |v .3a .|1+ .3b |
|00002c00| 11 31 73 69 6e 28 11 34 | 62 74 20 11 31 2b 20 11 |.1sin(.4|bt .1+ .|
|00002c10| 33 43 11 31 29 2c 20 77 | 68 65 72 65 20 11 33 43 |3C.1), w|here .3C|
|00002c20| 20 11 31 3d 20 61 72 63 | 74 61 6e 20 11 34 32 11 | .1= arc|tan .42.|
|00002c30| 31 2c 20 11 33 61 20 11 | 31 3e 20 30 0d 0b 00 20 |1, .3a .|1> 0... |
|00002c40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002c50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002c60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002c70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002c80| 20 20 11 33 61 0d 0a 00 | 0d 0a 00 20 20 20 20 20 | .3a...|... |
|00002c90| 11 31 0e 61 38 2d 34 2d | 34 39 61 0e 28 61 29 0f |.1.a8-4-|49a.(a).|
|00002ca0| 20 32 35 20 73 69 6e 20 | 28 35 11 34 74 20 11 31 | 25 sin |(5.4t .1|
|00002cb0| 2b 20 30 2e 36 34 33 35 | 29 0d 0a 00 0d 0b 00 20 |+ 0.6435|)...... |
|00002cc0| 20 20 20 20 0e 61 38 2d | 34 2d 34 39 62 0e 28 62 | .a8-|4-49b.(b|
|00002cd0| 29 0f 20 35 20 73 69 6e | 20 28 35 11 34 74 20 11 |). 5 sin| (5.4t .|
|00002ce0| 31 2b 20 30 2e 39 32 37 | 33 29 0d 0a 00 0d 0b 00 |1+ 0.927|3)......|
|00002cf0| 20 20 20 20 20 0e 61 38 | 2d 34 2d 34 39 63 0e 28 | .a8|-4-49c.(|
|00002d00| 63 29 0f 20 35 20 73 69 | 6e 20 28 35 11 34 74 20 |c). 5 si|n (5.4t |
|00002d10| 11 31 2b 20 30 2e 36 34 | 33 35 29 0d 0a 00 0d 0b |.1+ 0.64|35).....|
|00002d20| 00 20 20 20 20 20 0e 61 | 38 2d 34 2d 34 39 64 0e |. .a|8-4-49d.|
|00002d30| 28 64 29 0f 20 32 35 20 | 73 69 6e 20 28 35 11 34 |(d). 25 |sin (5.4|
|00002d40| 74 20 11 31 2b 20 30 2e | 39 32 37 33 29 0d 0a 00 |t .1+ 0.|9273)...|
|00002d50| 0d 0a 00 59 6f 75 20 6d | 61 79 20 77 61 6e 74 20 |...You m|ay want |
|00002d60| 74 6f 20 72 65 76 69 65 | 77 20 10 61 37 2d 34 2d |to revie|w .a7-4-|
|00002d70| 32 0e 69 37 2d 34 2d 33 | 0e 49 6e 74 65 67 72 61 |2.i7-4-3|.Integra|
|00002d80| 74 65 64 20 45 78 61 6d | 70 6c 65 20 33 2e 0f 0d |ted Exam|ple 3...|
|00002d90| 0a 00 53 65 63 74 69 6f | 6e 20 37 2e 34 20 20 53 |..Sectio|n 7.4 S|
|00002da0| 75 6d 20 61 6e 64 20 44 | 69 66 66 65 72 65 6e 63 |um and D|ifferenc|
|00002db0| 65 20 46 6f 72 6d 75 6c | 61 73 0d 0b 00 20 37 2e |e Formul|as... 7.|
|00002dc0| 20 20 46 69 6e 64 20 61 | 6c 6c 20 73 6f 6c 75 74 | Find a|ll solut|
|00002dd0| 69 6f 6e 73 20 69 6e 20 | 74 68 65 20 69 6e 74 65 |ions in |the inte|
|00002de0| 72 76 61 6c 20 5b 30 2c | 20 32 11 34 70 11 31 29 |rval [0,| 2.4p.1)|
|00002df0| 20 6f 66 20 0d 0a 00 20 | 20 20 20 20 20 20 20 20 | of ... | |
|00002e00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002e10| 20 20 20 20 11 34 70 20 | 20 20 20 20 20 20 20 20 | .4p | |
|00002e20| 20 20 20 70 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | p... | |
|00002e30| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 31 63 6f | | .1co|
|00002e40| 73 28 11 33 78 20 11 31 | 2b 20 11 34 32 11 31 29 |s(.3x .1|+ .42.1)|
|00002e50| 20 2d 20 63 6f 73 28 11 | 33 78 20 11 31 2d 20 11 | - cos(.|3x .1- .|
|00002e60| 34 32 11 31 29 20 3d 20 | 31 2e 0d 0b 00 20 20 20 |42.1) = |1.... |
|00002e70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002e80| 20 20 20 20 20 20 20 20 | 20 20 36 20 20 20 20 20 | | 6 |
|00002e90| 20 20 20 20 20 20 20 36 | 0d 0a 00 0d 0a 00 20 20 | 6|...... |
|00002ea0| 20 20 20 20 20 20 20 33 | 11 34 70 20 20 20 20 20 | 3|.4p |
|00002eb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002ec0| 20 20 20 20 20 20 20 20 | 20 20 70 20 20 11 31 33 | | p .13|
|00002ed0| 11 34 70 20 20 11 31 35 | 11 34 70 20 20 11 31 37 |.4p .15|.4p .17|
|00002ee0| 11 34 70 0d 0b 00 20 20 | 20 20 20 11 31 0e 61 38 |.4p... | .1.a8|
|00002ef0| 2d 34 2d 35 37 61 0e 28 | 61 29 0f 20 11 34 32 32 |-4-57a.(|a). .422|
|00002f00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002f10| 20 20 20 20 20 20 20 20 | 20 20 20 11 31 0e 61 38 | | .1.a8|
|00002f20| 2d 34 2d 35 37 62 0e 28 | 62 29 0f 20 11 34 32 11 |-4-57b.(|b). .42.|
|00002f30| 31 2c 20 11 34 32 32 11 | 31 2c 20 11 34 32 32 11 |1, .422.|1, .422.|
|00002f40| 31 2c 20 11 34 32 32 0d | 0b 00 20 20 20 20 20 20 |1, .422.|.. |
|00002f50| 20 20 20 20 11 31 32 20 | 20 20 20 20 20 20 20 20 | .12 | |
|00002f60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002f70| 20 20 20 20 20 20 32 20 | 20 20 32 20 20 20 32 20 | 2 | 2 2 |
|00002f80| 20 20 32 0d 0a 00 0d 0b | 00 20 20 20 20 20 20 20 | 2.....|. |
|00002f90| 20 20 11 34 70 20 20 11 | 31 33 11 34 70 20 20 20 | .4p .|13.4p |
|00002fa0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002fb0| 20 20 20 20 20 20 20 20 | 20 70 0d 0b 00 20 20 20 | | p... |
|00002fc0| 20 20 11 31 0e 61 38 2d | 34 2d 35 37 63 0e 28 63 | .1.a8-|4-57c.(c|
|00002fd0| 29 0f 20 11 34 32 11 31 | 2c 20 11 34 32 32 20 20 |). .42.1|, .422 |
|00002fe0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002ff0| 20 20 20 20 20 20 11 31 | 0e 61 38 2d 34 2d 35 37 | .1|.a8-4-57|
|00003000| 64 0e 28 64 29 0f 20 11 | 34 32 0d 0b 00 20 20 20 |d.(d). .|42... |
|00003010| 20 20 20 20 20 20 11 31 | 32 20 20 20 32 20 20 20 | .1|2 2 |
|00003020| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003030| 20 20 20 20 20 20 20 20 | 20 32 0d 0a 00 0d 0a 00 | | 2......|
|00003040| 59 6f 75 20 6d 61 79 20 | 77 61 6e 74 20 74 6f 20 |You may |want to |
|00003050| 72 65 76 69 65 77 20 10 | 61 37 2d 34 2d 32 0e 65 |review .|a7-4-2.e|
|00003060| 37 2d 34 2d 34 0e 47 75 | 69 64 65 64 20 45 78 61 |7-4-4.Gu|ided Exa|
|00003070| 6d 70 6c 65 20 34 2e 0f | 0d 0a 00 53 65 63 74 69 |mple 4..|...Secti|
|00003080| 6f 6e 20 37 2e 34 20 20 | 53 75 6d 20 61 6e 64 20 |on 7.4 |Sum and |
|00003090| 44 69 66 66 65 72 65 6e | 63 65 20 46 6f 72 6d 75 |Differen|ce Formu|
|000030a0| 6c 61 73 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |las... | |
|000030b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000030c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000030d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000030e0| 20 33 0d 0b 00 20 38 2e | 20 20 46 69 6e 64 20 74 | 3... 8.| Find t|
|000030f0| 68 65 20 65 78 61 63 74 | 20 76 61 6c 75 65 20 6f |he exact| value o|
|00003100| 66 20 73 69 6e 28 11 33 | 76 20 11 31 2b 20 11 33 |f sin(.3|v .1+ .3|
|00003110| 75 11 31 29 20 67 69 76 | 65 6e 20 74 68 61 74 20 |u.1) giv|en that |
|00003120| 73 69 6e 20 11 33 75 20 | 11 31 3d 20 11 34 32 11 |sin .3u |.1= .42.|
|00003130| 31 2c 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |1,... | |
|00003140| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003150| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003160| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003170| 35 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |5... | |
|00003180| 20 11 34 70 20 20 20 20 | 20 20 20 20 20 20 20 20 | .4p | |
|00003190| 20 20 20 20 11 31 35 20 | 20 11 34 70 0d 0b 00 20 | .15 | .4p... |
|000031a0| 20 20 20 20 11 31 30 20 | 3c 20 11 33 75 20 11 31 | .10 |< .3u .1|
|000031b0| 3c 20 11 34 32 11 31 2c | 20 61 6e 64 20 63 6f 73 |< .42.1,| and cos|
|000031c0| 20 11 33 76 20 11 31 3d | 20 2d 11 34 32 32 11 31 | .3v .1=| -.422.1|
|000031d0| 2c 20 11 34 32 20 11 31 | 3c 20 11 33 76 20 11 31 |, .42 .1|< .3v .1|
|000031e0| 3c 20 11 34 70 11 31 2e | 0d 0b 00 20 20 20 20 20 |< .4p.1.|... |
|000031f0| 20 20 20 20 20 20 20 20 | 32 20 20 20 20 20 20 20 | |2 |
|00003200| 20 20 20 20 20 20 20 20 | 31 33 20 20 32 0d 0a 00 | |13 2...|
|00003210| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 31 34 20 20 |... | 14 |
|00003220| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003230| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 31 36 0d | | 16.|
|00003240| 0b 00 20 20 20 20 20 0e | 61 38 2d 34 2d 32 33 61 |.. .|a8-4-23a|
|00003250| 0e 28 61 29 0f 20 11 34 | 32 32 20 20 20 20 20 20 |.(a). .4|22 |
|00003260| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003270| 20 20 20 20 20 11 31 0e | 61 38 2d 34 2d 32 33 62 | .1.|a8-4-23b|
|00003280| 0e 28 62 29 0f 20 11 34 | 32 32 0d 0b 00 20 20 20 |.(b). .4|22... |
|00003290| 20 20 20 20 20 20 11 31 | 36 35 20 20 20 20 20 20 | .1|65 |
|000032a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000032b0| 20 20 20 20 20 20 20 20 | 20 36 35 0d 0a 00 0d 0b | | 65.....|
|000032c0| 00 20 20 20 20 20 20 20 | 20 20 36 33 20 20 20 20 |. | 63 |
|000032d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000032e0| 20 20 20 20 20 20 20 20 | 20 20 20 33 33 0d 0b 00 | | 33...|
|000032f0| 20 20 20 20 20 0e 61 38 | 2d 34 2d 32 33 61 0e 28 | .a8|-4-23a.(|
|00003300| 63 29 0f 20 11 34 32 32 | 20 20 20 20 20 20 20 20 |c). .422| |
|00003310| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003320| 20 20 20 11 31 0e 61 38 | 2d 34 2d 32 33 64 0e 28 | .1.a8|-4-23d.(|
|00003330| 64 29 0f 20 11 34 32 32 | 0d 0b 00 20 20 20 20 20 |d). .422|... |
|00003340| 20 20 20 20 11 31 36 35 | 20 20 20 20 20 20 20 20 | .165| |
|00003350| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003360| 20 20 20 20 20 20 20 36 | 35 0d 0a 00 0d 0a 00 59 | 6|5......Y|
|00003370| 6f 75 20 6d 61 79 20 77 | 61 6e 74 20 74 6f 20 72 |ou may w|ant to r|
|00003380| 65 76 69 65 77 20 10 61 | 37 2d 34 2d 32 0e 69 37 |eview .a|7-4-2.i7|
|00003390| 2d 34 2d 31 0e 49 6e 74 | 65 67 72 61 74 65 64 20 |-4-1.Int|egrated |
|000033a0| 45 78 61 6d 70 6c 65 20 | 31 2e 0f 0d 0a 00 53 65 |Example |1.....Se|
|000033b0| 63 74 69 6f 6e 20 37 2e | 34 20 20 53 75 6d 20 61 |ction 7.|4 Sum a|
|000033c0| 6e 64 20 44 69 66 66 65 | 72 65 6e 63 65 20 46 6f |nd Diffe|rence Fo|
|000033d0| 72 6d 75 6c 61 73 0d 0b | 00 20 20 20 20 20 20 20 |rmulas..|. |
|000033e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000033f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003400| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003410| 20 20 20 20 20 37 0d 0b | 00 20 39 2e 20 20 46 69 | 7..|. 9. Fi|
|00003420| 6e 64 20 74 68 65 20 65 | 78 61 63 74 20 76 61 6c |nd the e|xact val|
|00003430| 75 65 20 6f 66 20 63 6f | 73 28 11 33 76 20 11 31 |ue of co|s(.3v .1|
|00003440| 2d 20 11 33 75 11 31 29 | 20 67 69 76 65 6e 20 74 |- .3u.1)| given t|
|00003450| 68 61 74 20 73 69 6e 20 | 11 33 75 20 11 31 3d 20 |hat sin |.3u .1= |
|00003460| 11 34 32 32 11 31 2c 0d | 0b 00 20 20 20 20 20 20 |.422.1,.|.. |
|00003470| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003480| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003490| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000034a0| 20 20 20 20 20 32 35 0d | 0a 00 20 20 20 20 20 11 | 25.|.. .|
|000034b0| 34 70 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |4p | |
|000034c0| 20 20 20 20 20 20 20 11 | 31 34 20 20 33 11 34 70 | .|14 3.4p|
|000034d0| 0d 0b 00 20 20 20 20 20 | 32 20 11 31 3c 20 11 33 |... |2 .1< .3|
|000034e0| 75 20 11 31 3c 20 11 34 | 70 20 11 31 61 6e 64 20 |u .1< .4|p .1and |
|000034f0| 63 6f 73 20 11 33 76 20 | 11 31 3d 20 11 34 32 11 |cos .3v |.1= .42.|
|00003500| 31 2c 20 11 34 32 32 20 | 11 31 3c 20 11 33 76 20 |1, .422 |.1< .3v |
|00003510| 11 31 3c 20 32 11 34 70 | 11 31 2e 0d 0b 00 20 20 |.1< 2.4p|.1.... |
|00003520| 20 20 20 32 20 20 20 20 | 20 20 20 20 20 20 20 20 | 2 | |
|00003530| 20 20 20 20 20 20 20 20 | 20 35 20 20 20 32 0d 0a | | 5 2..|
|00003540| 00 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 34 34 |.... | 44|
|00003550| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003560| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 34 0d | | 4.|
|00003570| 0b 00 20 20 20 20 20 0e | 61 38 2d 34 2d 32 37 61 |.. .|a8-4-27a|
|00003580| 0e 28 61 29 0f 20 11 34 | 32 32 32 20 20 20 20 20 |.(a). .4|222 |
|00003590| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000035a0| 20 20 20 20 20 11 31 0e | 61 38 2d 34 2d 32 37 62 | .1.|a8-4-27b|
|000035b0| 0e 28 62 29 0f 20 11 34 | 32 0d 0b 00 20 20 20 20 |.(b). .4|2... |
|000035c0| 20 20 20 20 20 11 31 31 | 32 35 20 20 20 20 20 20 | .11|25 |
|000035d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000035e0| 20 20 20 20 20 20 20 20 | 35 0d 0a 00 0d 0b 00 20 | |5...... |
|000035f0| 20 20 20 20 20 20 20 20 | 20 31 31 37 20 20 20 20 | | 117 |
|00003600| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003610| 20 20 20 20 20 20 20 20 | 20 20 34 38 0d 0b 00 20 | | 48... |
|00003620| 20 20 20 20 0e 61 38 2d | 34 2d 32 37 63 0e 28 63 | .a8-|4-27c.(c|
|00003630| 29 0f 20 2d 11 34 32 32 | 32 20 20 20 20 20 20 20 |). -.422|2 |
|00003640| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003650| 20 20 11 31 0e 61 38 2d | 34 2d 32 37 62 0e 28 64 | .1.a8-|4-27b.(d|
|00003660| 29 0f 20 11 34 32 32 32 | 0d 0b 00 20 20 20 20 20 |). .4222|... |
|00003670| 20 20 20 20 20 11 31 31 | 32 35 20 20 20 20 20 20 | .11|25 |
|00003680| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003690| 20 20 20 20 20 20 20 31 | 32 35 0d 0a 00 0d 0a 00 | 1|25......|
|000036a0| 59 6f 75 20 6d 61 79 20 | 77 61 6e 74 20 74 6f 20 |You may |want to |
|000036b0| 72 65 76 69 65 77 20 10 | 61 37 2d 34 2d 32 0e 69 |review .|a7-4-2.i|
|000036c0| 37 2d 34 2d 32 0e 49 6e | 74 65 67 72 61 74 65 64 |7-4-2.In|tegrated|
|000036d0| 20 45 78 61 6d 70 6c 65 | 20 32 2e 0f 0d 0a 00 14 | Example| 2......|
|000036e0| 00 00 00 73 00 00 00 50 | 00 04 00 14 00 00 00 10 |...s...P|........|
|000036f0| 00 00 00 61 38 2d 34 2d | 31 31 61 00 8b 00 00 00 |...a8-4-|11a.....|
|00003700| da 00 00 00 50 00 04 00 | 8b 00 00 00 87 00 00 00 |....P...|........|
|00003710| 61 38 2d 34 2d 31 31 63 | 00 69 01 00 00 e2 00 00 |a8-4-11c|.i......|
|00003720| 00 50 00 04 00 69 01 00 | 00 65 01 00 00 61 38 2d |.P...i..|.e...a8-|
|00003730| 34 2d 31 35 61 00 4f 02 | 00 00 8d 00 00 00 50 00 |4-15a.O.|......P.|
|00003740| 04 00 4f 02 00 00 4b 02 | 00 00 61 38 2d 34 2d 31 |..O...K.|..a8-4-1|
|00003750| 35 62 00 e0 02 00 00 96 | 00 00 00 50 00 04 00 e0 |5b......|...P....|
|00003760| 02 00 00 dc 02 00 00 61 | 38 2d 34 2d 31 35 63 00 |.......a|8-4-15c.|
|00003770| 7a 03 00 00 5f 00 00 00 | 50 00 04 00 7a 03 00 00 |z..._...|P...z...|
|00003780| 76 03 00 00 61 38 2d 34 | 2d 31 35 64 00 dd 03 00 |v...a8-4|-15d....|
|00003790| 00 c8 00 00 00 50 00 04 | 00 dd 03 00 00 d9 03 00 |.....P..|........|
|000037a0| 00 61 38 2d 34 2d 31 39 | 61 00 a9 04 00 00 8a 00 |.a8-4-19|a.......|
|000037b0| 00 00 50 00 04 00 a9 04 | 00 00 a5 04 00 00 61 38 |..P.....|......a8|
|000037c0| 2d 34 2d 31 39 62 00 37 | 05 00 00 67 00 00 00 50 |-4-19b.7|...g...P|
|000037d0| 00 04 00 37 05 00 00 33 | 05 00 00 61 38 2d 34 2d |...7...3|...a8-4-|
|000037e0| 31 39 63 00 a2 05 00 00 | b0 00 00 00 50 00 04 00 |19c.....|....P...|
|000037f0| a2 05 00 00 9e 05 00 00 | 61 38 2d 34 2d 31 39 64 |........|a8-4-19d|
|00003800| 00 56 06 00 00 17 03 00 | 00 50 00 04 00 56 06 00 |.V......|.P...V..|
|00003810| 00 52 06 00 00 61 38 2d | 34 2d 32 33 61 00 71 09 |.R...a8-|4-23a.q.|
|00003820| 00 00 8a 00 00 00 50 00 | 04 00 71 09 00 00 6d 09 |......P.|..q...m.|
|00003830| 00 00 61 38 2d 34 2d 32 | 33 62 00 ff 09 00 00 0e |..a8-4-2|3b......|
|00003840| 00 00 00 50 00 04 00 ff | 09 00 00 fb 09 00 00 61 |...P....|.......a|
|00003850| 38 2d 34 2d 32 33 64 00 | 11 0a 00 00 a7 00 00 00 |8-4-23d.|........|
|00003860| 50 00 04 00 11 0a 00 00 | 0d 0a 00 00 61 38 2d 34 |P.......|....a8-4|
|00003870| 2d 32 37 61 00 bc 0a 00 | 00 41 02 00 00 50 00 04 |-27a....|.A...P..|
|00003880| 00 bc 0a 00 00 b8 0a 00 | 00 61 38 2d 34 2d 32 37 |........|.a8-4-27|
|00003890| 62 00 01 0d 00 00 0e 00 | 00 00 50 00 04 00 01 0d |b.......|..P.....|
|000038a0| 00 00 fd 0c 00 00 61 38 | 2d 34 2d 32 37 63 00 13 |......a8|-4-27c..|
|000038b0| 0d 00 00 a5 00 00 00 50 | 00 04 00 13 0d 00 00 0f |.......P|........|
|000038c0| 0d 00 00 61 38 2d 34 2d | 34 39 61 00 bc 0d 00 00 |...a8-4-|49a.....|
|000038d0| 93 00 00 00 50 00 04 00 | bc 0d 00 00 b8 0d 00 00 |....P...|........|
|000038e0| 61 38 2d 34 2d 34 39 62 | 00 53 0e 00 00 e2 00 00 |a8-4-49b|.S......|
|000038f0| 00 50 00 04 00 53 0e 00 | 00 4f 0e 00 00 61 38 2d |.P...S..|.O...a8-|
|00003900| 34 2d 34 39 63 00 39 0f | 00 00 45 01 00 00 50 00 |4-49c.9.|..E...P.|
|00003910| 04 00 39 0f 00 00 35 0f | 00 00 61 38 2d 34 2d 34 |..9...5.|..a8-4-4|
|00003920| 39 64 00 82 10 00 00 ab | 00 00 00 50 00 04 00 82 |9d......|...P....|
|00003930| 10 00 00 7e 10 00 00 61 | 38 2d 34 2d 35 33 61 00 |...~...a|8-4-53a.|
|00003940| 31 11 00 00 7c 01 00 00 | 50 00 04 00 31 11 00 00 |1...|...|P...1...|
|00003950| 2d 11 00 00 61 38 2d 34 | 2d 35 33 62 00 b1 12 00 |-...a8-4|-53b....|
|00003960| 00 7a 00 00 00 50 00 04 | 00 b1 12 00 00 ad 12 00 |.z...P..|........|
|00003970| 00 61 38 2d 34 2d 35 33 | 63 00 2f 13 00 00 78 01 |.a8-4-53|c./...x.|
|00003980| 00 00 50 00 04 00 2f 13 | 00 00 2b 13 00 00 61 38 |..P.../.|..+...a8|
|00003990| 2d 34 2d 35 33 64 00 ab | 14 00 00 43 00 00 00 50 |-4-53d..|...C...P|
|000039a0| 00 04 00 ab 14 00 00 a7 | 14 00 00 61 38 2d 34 2d |........|...a8-4-|
|000039b0| 35 37 61 00 f2 14 00 00 | a3 01 00 00 50 00 04 00 |57a.....|....P...|
|000039c0| f2 14 00 00 ee 14 00 00 | 61 38 2d 34 2d 35 37 62 |........|a8-4-57b|
|000039d0| 00 99 16 00 00 0b 01 00 | 00 50 00 04 00 99 16 00 |........|.P......|
|000039e0| 00 95 16 00 00 61 38 2d | 34 2d 35 37 63 00 a8 17 |.....a8-|4-57c...|
|000039f0| 00 00 ff 00 00 00 50 00 | 04 00 a8 17 00 00 a4 17 |......P.|........|
|00003a00| 00 00 61 38 2d 34 2d 35 | 37 64 00 ab 18 00 00 98 |..a8-4-5|7d......|
|00003a10| 01 00 00 50 00 04 00 ab | 18 00 00 a7 18 00 00 61 |...P....|.......a|
|00003a20| 38 2d 34 2d 35 61 00 47 | 1a 00 00 6e 01 00 00 50 |8-4-5a.G|...n...P|
|00003a30| 00 04 00 47 1a 00 00 43 | 1a 00 00 61 38 2d 34 2d |...G...C|...a8-4-|
|00003a40| 35 62 00 b9 1b 00 00 4f | 02 00 00 50 00 04 00 b9 |5b.....O|...P....|
|00003a50| 1b 00 00 b5 1b 00 00 61 | 38 2d 34 2d 35 63 00 0c |.......a|8-4-5c..|
|00003a60| 1e 00 00 45 00 00 00 50 | 00 04 00 0c 1e 00 00 08 |...E...P|........|
|00003a70| 1e 00 00 61 38 2d 34 2d | 35 64 00 79 1e 00 00 58 |...a8-4-|5d.y...X|
|00003a80| 01 00 00 4d 28 00 00 51 | 1e 00 00 00 00 00 00 78 |...M(..Q|.......x|
|00003a90| 37 2d 34 00 f9 1f 00 00 | 78 02 00 00 4d 28 00 00 |7-4.....|x...M(..|
|00003aa0| d1 1f 00 00 00 00 00 00 | 78 37 2d 34 2d 31 00 99 |........|x7-4-1..|
|00003ab0| 22 00 00 b2 01 00 00 4d | 28 00 00 71 22 00 00 00 |"......M|(..q"...|
|00003ac0| 00 00 00 78 37 2d 34 2d | 32 00 73 24 00 00 0b 02 |...x7-4-|2.s$....|
|00003ad0| 00 00 4d 28 00 00 4b 24 | 00 00 00 00 00 00 78 37 |..M(..K$|......x7|
|00003ae0| 2d 34 2d 33 00 a6 26 00 | 00 90 01 00 00 4d 28 00 |-4-3..&.|.....M(.|
|00003af0| 00 7e 26 00 00 00 00 00 | 00 78 37 2d 34 2d 34 00 |.~&.....|.x7-4-4.|
|00003b00| 5e 28 00 00 d0 01 00 00 | 4d 28 00 00 36 28 00 00 |^(......|M(..6(..|
|00003b10| 00 00 00 00 78 37 2d 34 | 2d 35 00 56 2a 00 00 3c |....x7-4|-5.V*..<|
|00003b20| 03 00 00 4d 28 00 00 2e | 2a 00 00 00 00 00 00 78 |...M(...|*......x|
|00003b30| 37 2d 34 2d 36 00 ba 2d | 00 00 c1 02 00 00 4d 28 |7-4-6..-|......M(|
|00003b40| 00 00 92 2d 00 00 00 00 | 00 00 78 37 2d 34 2d 37 |...-....|..x7-4-7|
|00003b50| 00 a3 30 00 00 0b 03 00 | 00 4d 28 00 00 7b 30 00 |..0.....|.M(..{0.|
|00003b60| 00 00 00 00 00 78 37 2d | 34 2d 38 00 d6 33 00 00 |.....x7-|4-8..3..|
|00003b70| 09 03 00 00 4d 28 00 00 | ae 33 00 00 00 00 00 00 |....M(..|.3......|
|00003b80| 78 37 2d 34 2d 39 00 | |x7-4-9. | |
+--------+-------------------------+-------------------------+--------+--------+
