Find sin2x, cos2x, and tan2x if cosx= 15/17

Question

Find sin2x, cos2x, and tan2x if cosx= 15/17 and x terminates in quadrant IV.

Sin2x = ?

Cos2x = ?

Tan2x = ?

Answer 1

sin(2x) = 2 sin(x) cos(x) = 2 ( -8/17)(15/16) = -240/289

cos(2x) = 1 - 2* sin^2(x) = 1 - 2 (-8/17)^2 = 1 - 2(64/289) = 1 - 128/289 = 161/289

tan(2x) = 2 tanx / (1-tan^2(x)) = 2 * (-8/15) / ( 1 - (-8/15)^2)

= -16/15 / ( (225 - 64)/225

=16/15 * 225/161 = 240/161