Question

What is theta +2kpi in trigonometry

Answer 1

`\theta` often denotes an angle, where
`0\le\theta<2\pi` is conventionally used.

Adding
`2k\pi`, where
`k` is any integer, is the same as saying that
`\theta` is equivalent to
`\theta\pm2\pi,\theta\pm4\pi,\theta\pm6\pi` etc.

This is the case because a complete revolution has an angle measure of
`2\pi`, which means that adding any multiple of
`2\pi` to a given angle results in the same angle.

Example:

If
`\theta=\pi`, then
`\cos\pi=-1`. This is also true if
`\theta=\pi+2\pi=3\pi`, which gives
`\cos3\pi=\cos(\pi+2\pi)=\cos\pi\cos2\pi-\sin\pi\sin2\pi=(-1)(1)-(0)(0)=-1`.