CPM Homework Help : PC Problem 7-26

Determine if the tangent function is even, odd, or neither. Show your result graphically as well as algebraically.

Hint:

Even:
$f\left(x\right) = f\left(−x\right)$

Odd:
$−f\left(x\right) = f\left(−x\right)$

Answer:

Tangent is odd.

$\tan (-x)=\frac{\sin(-x)}{\cos(-x)}=\frac{-\sin x}{\cos x}=-\frac{\sin x}{\cos x}=-\tan x$