Question

if 90 degrees < theta < 180 degrees and cos theta = -4/5, find sin 4 theta

Answer 1

If you know the double angle formula, you can change sin(4 theta) into 2sin(2theta)cos(2theta) which can be further change into
2(2sin(theta)cos(theta))*(cos^2(theta)-sin^2(theta))

Answer 2

how did you come up with second expression?

Answer 3

You are given cos(theta) so you can find sin(theta) using right triangles