# How do you solve cos^2theta=1?

Nov 25, 2016

First take the square root of both sides.

$\sqrt{{\cos}^{2} \theta} = \sqrt{1}$

Simplify, and don't forget the $\pm$!

$\cos \theta = \pm 1$

Now think back to the unit circle and find the values where $\cos$ (x-values) is equal to $\pm 1$.

$\theta = 0 , \pi$

Those are the answers in the range from $0$ to $2 \pi$ (which is one unit circle), but if you want all solutions (like every single one), then it would look like:

$\theta = 2 \pi n , \pi + 2 \pi n$