Question

Why is it that you divide the angle value in the trig function by `2pi` to get the period?

Answer 1

This is because a complete rotation represents `2pi` radians.

Explanation:

We measure angles anticlockwise from `x`-axis and call these positive angles. Now as we rotate, angle (in radians) increases up to `2pi` and after that it just repeats in the cycle of `2pi` and hence trigonometric ratios too repeat.

Hence when we divide the angle by `2pi`, the trigonometric ratio of the remainder is same as that of the complete angle.