find every angle theta with 0<= theta <= 2pi radians, and 2 sin^2(theta)+cos(theta)=2

Question

This is a question from a calculus 1 class. I have no idea how to tackle this question.

Answer 1

sin^2=1- cos^2, so using x as theta, 2-2cos^2x+cosx=2; 2cos^2x-cosx=0; cosx(2cosx-1)=0; cos x=0 or 0.5. x=(pi)/3 or 60°, (pi)/2 or 90°, 3(pi)/2 or 270°, 5(pi)/3 or 300°.