Is Sine An Even Function?
Explanation of why sine is an even function:
Sine is an odd function, and cosine is an even function.
A function is said to be an odd function if for any number , . A function is said to be an even function if for any number , .
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 is the same angle as except it’s on the other side of the x-axis. Flipping a point to the other side of the x-axis makes it into , 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.