Find sin 2x, cos 2x, and tan 2x

Question

 if sin x = -15/17 and x terminates in quadrant IV?

Answer 1

sin(x) = -15/17

From pythagorean theorem adjacent side is 8.

In fourth quadrant cos(x) is positive.

cos(x) = 8/17

Recall the double angle formulae

sin(2x) = 2 sin(x) cos(x)

= 2(-15/17)(8/17)

sin(2x) = - 240/289

cos(2x) = cos²(x) - sin²(x)

= (8/17)² - (-15/17)²

= 64/289 - 225/289

cos(2x) = - 161/289

Tan(2x) = sin(2x)/cos(2x)

= [- 240/289]/[- 161/289]

Tan(2x) = 240/161