Trigonometric Functions

The symbols used for the six basic trigonometric functions—sin, cos, tan, cot, sec, csc—are abbreviations for the words cosine, sine, tangent, cotangent, secant, and cosecant, respectively.


You can enter these trigonometric functions and many other functions either from the keyboard in mathematics mode or from the dialog box that drops down when you click itbpF0.3009in0.3009in0.0701infunction.wmf or choose Insert + Math Name. When you enter one of these functions from the keyboard in mathematics mode, the function name automatrically turns gray when you type the final letter of the name.

Note    Ordinary functions require parentheses around the function argument, while trigonometric functions commonly do not. Scientific Notebook allows trigonometric functions without parentheses. If you believe parentheses should be required for all functions, you can change this behavior in the Maple Settings dialog. Click the Definition Options tab and under Function Argument Selection Method, check Convert Trigtype to Ordinary.

To find values of the trigonometric functions, use Evaluate or Evaluate Numerically.

$\blacktriangleright$ Evaluate

sin${\frac{{3\pi }}{{4}}}$ = ${\frac{{1}}{{2}}}$$\sqrt{{2}}$

sin$\left(\vphantom{ 1}\right.$1$\left.\vphantom{ 1}\right)$ = sin 1

sin 60o = ${\frac{{1}}{{2}}}$$\sqrt{{3}}$

$\blacktriangleright$ Evaluate Numerically

sin${\frac{{3\pi }}{{4}}}$ = . 70711

sin$\left(\vphantom{ 1}\right.$1$\left.\vphantom{ 1}\right)$ = . 84147

sin 60o = . 86603

The notation you use determines whether the argument is interpreted as radians or degrees: sin 30 = - .98803, and sin 30o =  .5. The symbol used for degrees is the small circle that appears on the Common Symbols toolbar and on the Binary Operations symbol panel. It should be typed in a superscript. All operations will convert angle measure to radians. Click radians to degreesRadians to degrees for a discussion of conversion. Click Units in Scientific NotebookDM2-6.tex#Units for a discussion of units that can be used for plane angles.

Your choice for Digits Used in Display in the Maple + Settings or Mathematica + Settings dialog box determines the number of places displayed in the response to Evaluate Numerically.

Expression Evaluate Evaluate Numerically
sin${\frac{{\pi }}{{4}}}$


 ${\frac{{1}}{{2}}}$$\sqrt{{2}}$ .70711
sin 14o37′  sin${\dfrac{{877}}{{10800}}}$π


 

  .25235
log10sin x


 ${\dfrac{{\ln \left( \sin x\right) }}{{\ln 2+\ln 5}}}$  .43429 ln$\left(\vphantom{ \sin x}\right.$sin x$\left.\vphantom{ \sin x}\right)$
3o54′  ${\dfrac{{13}}{{600}}}$π  6.8068×10-2