Question

What is theta +2kpi in trigonometry

Answer 1

$\theta$ often denotes an angle, where $0\le\theta$ 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 $\cos3\pi=\cos(\pi+2\pi)=\cos\pi\cos2\pi-\sin\pi\sin2\pi=(-1)(1)-(0)(0)=-1$.