# Is the function f(x) = sin x even, odd or neither?

Oct 31, 2015

Odd

#### Explanation:

By definition, a function f is even if $f \left(- x\right) = f \left(x\right)$.
A function f is odd if $f \left(- x\right) = - f \left(x\right)$

Since $\sin \left(- x\right) = - \sin x$, it implies that sinx is an odd function.

That is why for example a half range Fourier sine series is said to be odd as well since it is an infinite sum of odd functions.