# How do you determine if f(x)= tan x is an even or odd function?

Aug 6, 2016

$\tan x$ is odd.

#### Explanation:

If function is even, then $f \left(- x\right) = f \left(x\right)$

If odd, $f \left(- x\right) = - f \left(x\right)$.

Recall that $\tan x = \frac{\sin x}{\cos x}$

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

$\tan x$ is odd.