Question

Is Sine An Even Function?

Answer 1

Explanation of why sine is an even function:

Sine is an odd function, and cosine is an even function.

A function $f$ is said to be an odd function if for any number $x$, $f(–x)=–f\left(x\right)$. A function $f$ is said to be an even function if for any number $x$, $f(–x)=f\left(x\right)$.

Sine is an odd function, and cosine is an even function.

sin (–θ) = –sin θ

cos (–θ) = cos θ.

These facts follow from the symmetry of the unit circle across the x-axis. The angle $-t$ is the same angle as $t$ except it’s on the other side of the x-axis. Flipping a point $(x,y)$ to the other side of the x-axis makes it into $(x,–y)$, so the y-coordinate is negated, that is, the sine is negated, but the x-coordinate remains the same, that is, the cosine is unchanged.

Hence, Sine is not an Even Function.