Question

How do you find the exact value of the expression sin 2x, cos 2x, and tan 2x given `Sin x = 12/13` where x lies on Quadrant I?

Answer 1

sin x = 12/13

`cos^2 x = 1 - sin^2 x = 1 - 144/169 = 25/169 -> cos x = 5/13`

`sin 2x = 2sin x.cos x = 2(12/13)(5/13) = (120)/(169) = 0/71`

`cos 2x = 2cos^2 x - 1 = -119/169 = - 0.70`

`tan 2x = +- 0.71/-0.70 = - 1`