Question

How do you find the exact value of cos2x using the double angle formula given `cosx=-2/13`, `pi/2<x<pi`?

Answer 1

Use the trig identity:`cos 2x = 2cos^2 x - 1`

`cos 2x = 2(-2/13)^2 - 1 = -161/169 = -0.95`

Note . `cos x = -2/13 --> x = 98,85` (Quadrant II) -->
2x = 197.70. (Quadrant III) #

cos 2x = -0.95 gives 2 arcs with same cos value:
2x = 161.80 (Quadrant II) (rejected) and 2x = 198.0 (Quadrant III). OK