Question

How/Why do you get the solutions to a trigonometry equation with multiple angles?

Explain why the solutions to `cos(2x)=((sqrt(2))/2)` of the interval `[0,2pi)` are what they are!

Answer 1

For the example `cos(2x)=(sqrt2/2)`, the reason the answers `{pi/4, (7pi)/4, (9pi)/4, (15pi)/4}` are in the first and fourth quadrant are because cosine is positive in those quadrants. That is what is asking for.

Explanation:

Realized my mistake and answered my own question. I had not realized it was a cosine and wasn't thinking about the quadrants.