Math homework dealing with trigonometry

Question

Solve each equation for 0 less than or equal to theta which is less than 2 pi.

1. -2sin( theta)= square root of 2
2. cos^2 x= 1/4
3. sin(2x)=1

Answer 1

1. sin(theta) = sqr2/2 that is a common angle = 45 degrees but in quadrant 3 or 4, so theta equals 180 plus 45 = 225 degrees or 360 minus 45 = 315 degrees = 7pi/4
2. take square roots, to get cos2x = 1/2, 2x = 60, x = 30 degrees = pi/6
3. 2x = 90, x = 45 degrees = pi/4