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

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Answer 1 · 2016-08-06T19:50:55

$tanx$ is odd.

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

If odd, $f(-x) = -f(x)$ .

Recall that $tanx = (sinx)/(cosx)$

$f(-x) = (sin(-x))/(cos(-x)) = (-sin(x))/(cos(x)) = -tan(x) = -f(x)$

$tanx$ is odd.

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