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

Question

41731 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-31T13:31:49

Odd

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 $sin (- x) = - sin x$ $sin(-x)=-sinx$ , 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.

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