Given that cosine of theta equals 8 over 17 and that θ lies in Quadrant IV, what is the exact value of sin 2θ?

Question

Given that  and that θ lies in Quadrant IV, what is the exact value of sin 2θ?

Answer 1

17^2 -8^2 = 289-64 = 225 = 15^2

cosT = 8/17, sinT = -15/17

sin2T = 2sinTcosT = 2(15/17)(8/17) = 240/289

sin2T = 240/289

check the answer

cosT =8/17

T = about -61.93

2T = about -123.86

sin-123.86= about -.83

-240/289 = about -.83