Labels:text | screenshot | black and white | graphics | graphic design OCR: Figure 12-11: Illustration of the Range of the Tangent Function The usual graph of tan as a real function looks like an infinite chorus line of disco dancers, left hands pointed skyward and right hands to the floor. The tan function is the quotient of sin and cos but it doesn't much look like either except for having period 2x. This goes for the complex plane as well, although the awoopy loops produced from the ammulus between w/2 and 2 look vaguely like those from the graph of ein inside out. The real axis is mapped onto itself with infinite multiplicity (period 2x). The imaginary axis is mapped backwards onto [-i, {]: +oot is mapped lo - s and -sos to +3. Horizontal lines below or above the real axis become circles surrounding +i or -i, respectively. Vertical lines become circular arce from +i lo -i; two vertical lines separated by (2% + 1)x for integer & together become a complete circle. It seems that two arce shown hit the real axis at _x /2 = = 1.57 ... but that is a coincidence; they really hit the axis at + lan ] = 1.55 ..
