"If sin x = sqrt 2/2, and cos x = - sqrt2/2, then x = ...?" How do I do problems like this?

Question

Could someone explain to me the mathematical process to solve this problem?

a) pi/4 b) 3pi/4 c) 5pi/4 d) 7pi/4

Thanks!

sorry, is (sqrt 2)/2 and - (sqrt 2)/2

Answer 1

1.) Whenever you see sin or cos x = √2/2, it's a 45 degree angle of some sort.
2.) sin is positive from 0 to π, and cos is positive from 0 to π/2 and 3π/2 to 2π.

Given that:
If sin x = √2/2, then it's a 45 or 135 degree angle.
If cos x = -√2/2, then it is a 135 or 225 degree angle.

So x = 135 degrees = 3π/4