cos ( 2θ ) = 0.34 The angle 2θ is in quadrant IV sin ( θ ) =?

Question

Using a double-angle or half-angle formula to find  

Answer 1

cos(theta) = sqr((1+.34)/2) = sqr(1.34/2) = sqr(0.67) = .819

sin(theta) = square root of (1-cos^2(theta)

sin(theta) = sqr(1-.67) = sqr(.33) = 0.57

theta = -70.1 = 360-70.1 = 289.9

half theta = 145

sin145 = 0.57

it helps to work it 2 different ways and get the same answer