Question

Solve each equation for 0<_ 0<_ 2pi(3.14)
A) 2cos^20 - sin0 -1=0
My answers: sin0= -1/2 or sin0=1 so 0 = 7pi/6, 11pi/6 and pi/2

But the back of the book says: pi/6, 5pi/6 and 3pi/2

Answer 1

2-2sin^2-sin-1=0
2sin^2+sin-1 = 0
(2sin-1)(sin+1) = 0
sin = 1/2 or -1
sin = 1/2 at pi/6 and 5pi/6
sin = -1 at 3pi/2

Better check your factoring.
Your angles are correct for the values you obtained, but those values had the wrong signs, and hence, the wrong sines :-)