Question
Solve the equation cos2θ = 1/2sinθ 0º≤θ≤90º. (Hint: Graph each side of the equation and determine where the graphs intersect.)
Answers
Steve
cos2θ = 1 - 2sin^2 θ
so,
1 - 2sin^2 θ = 1/2 sinθ
4 sin^2θ + sinθ - 2 = 0
Now just use the quadratic formula to solve for sinθ, then take the arcsin. To check your answer, see
http://www.wolframalpha.com/input/?i=cos2%CE%B8+%3D+1%2F2+sin%CE%B8
so,
1 - 2sin^2 θ = 1/2 sinθ
4 sin^2θ + sinθ - 2 = 0
Now just use the quadratic formula to solve for sinθ, then take the arcsin. To check your answer, see
http://www.wolframalpha.com/input/?i=cos2%CE%B8+%3D+1%2F2+sin%CE%B8