# Math Help - Equivalent angle

1. ## Equivalent angle

Hi guys, My professor keeps talking about "equivalent angles" So, if we want to find the square root of a rotation matrix, A(r,theta)^n, we can "replace theta by the EQUIVALENT angle theta + 2pi. We can go further to theta + 4 pi, theta + 6pi and so on until we come full circle to theta + 2npi which gives us the same root we started with."

I cant visualize

"replace theta by the EQUIVALENT angle theta + 2pi. We can go further to theta + 4 pi, theta + 6pi and so on until we come full circle to theta + 2npi which gives us the same root we started with."

on the unit circle, and am unsure how it goes full circle. Wouldn't adding 2pi to any angle bring it full circle?

2. ## Re: Equivalent angle

Originally Posted by sfspitfire23
Hi guys, My professor keeps talking about "equivalent angles" So, if we want to find the square root of a rotation matrix, A(r,theta)^n, we can "replace theta by the EQUIVALENT angle theta + 2pi. We can go further to theta + 4 pi, theta + 6pi and so on until we come full circle to theta + 2npi which gives us the same root we started with."
This is the sort of question that can be dangerous to answer.
It is true that $\sin(\theta)=\sin(\theta+2\pi)$ but $\theta\ne\theta+2\pi$.
If you use functions and appropriate cycles.