Find cos 2theta

Question

If cos theta = 24/25 and 3pi/2 < theta < 2pi, then what is cos 2 theta? I think I figured it out using double agent, but I just want to check my answer, and it's kind of hard to look up.

Answer 1

We can use the double angle cosine formula here:

cos(2θ) = 1 - 2(sinθ)²

Since cosθ is 24/25, we can infer the length of the third side since 24,25 is part of a pythagorean triple of 7,24,25. So sinθ = -7/25 (negative because θ is in the fourth quadrant).

So cos(2θ) = 1 - 2(-7/25)² = 527/625