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

1 Answer
Oct 31, 2015

Odd

Explanation:

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

Since sin(-x)=-sinxsin(x)=sinx, 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.