Question

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

Answer 1

First take the square root of both sides.

`sqrt(cos^2theta) = sqrt1`

Simplify, and don't forget the `+-`!

`costheta = +-1`

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

`theta = 0, pi`

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

`theta = 2pin, pi + 2pin`