Solve the trigonometric equation in the interval [0, 2𝜋). Give the exact value, if possible; otherwise, round your answer to two decimal places. 2 cos2(𝜃) + 11 cos(𝜃) + 5 = 0

Answer 1

Make a substitution. Let x = cos(θ).

The equation after substitution becomes 2x² + 11x + 5 = 0.

Solve for x:

2x² + 10x + x + 5 = 0

(x + 5)(2x + 1) = 0

x = -1/2

x = -5

Plug cos(θ) back in for x

cos(θ) = -5

cos(θ) = -1/2

cos(θ) can't equal -5 so therefore cos(θ) = -1/2

Solve for θ