Double Angle Identity

Question

Find the values of sin 2 theta, cos 2 theta, and tan 2 theta for the interval of pi and 3 pi over 2 when cos theta equals negative 5 over 13.

Answer 1

Given Costheta = -5/13

For the interval 180 and 270

Sintheta = -12/13

Tan theta = 5/12

Sin2theta = 2 Sintheta Costheta

= 2*-12/13*-5/13

= 120/169

Cos2theta = Cos^2a-Sin^2a = 25/169-144/169 = -119/169

tan2theta = Sin2theta/Costheta

= (120/169)/(-119/169)

= -120/119