How Do You Solve for Theta in Degrees When Given a Cosine Squared Equation?

[huskerfan5788]

This may seem really simple, but I just can't figure out how to do it.

Say you have an equation 0.651 = cos² (theta)

How would you solve for theta in degrees? I know that for cos (theta) you take the arccos, but what do you do when it is squared?

Thank you!

 

[SteamKing]

I don't know. Maybe take square roots of both sides first?

 

[edgepflow]

And after you take the square root of both sides, consider taking the arc cosine (also called inverse cosine) of both sides.

 

[micromass]

Be warned that taking the square root is not enough. You'll also need to take the negative square root if you don't want to lose information...

 

[QuarkCharmer]

If you just treat it like a quadratic I don't think you will lose any information.
0.651 = cos²
cos² - 0.651 = 0
cos² - 0cos - 0.651 = 0

Then you can solve for cos(theta) = +/-Something via arccos. I guess that's really the same as what was mentioned above though.