Question

Cos(theta)=(15/17), and sin>0; How do I solve for 2theta?

Answer 1

Use the trig identities:
a) cos 2a = 2*cos^2 a -1. Replace cos a by 15/17
cos 2a = 2*(225/289) - 1 = 1.58 - 1 = 0.58
b) sin^2 a + cos^2 a = 1
sin^2 a = 1 - cos^2 a= 1 - (225/289) = 1 - 0.78 = 0.22
sin a = V(0.22) = 0.47.
c) sin 2a = 2*sin a*cos a = 2(0.47)(15/17) = ......