-2sin^2(a)-cos(a)=-1

Question

Find all solutions to the equation below in the interval

Give all answers as decimals rounded to 3 places

-2sin^2(a)-cos(a)=-1

Answer 1

-2sin²a - cosa = -1

-2(1 - cos²a) - cosa = -1

2cos²a - cosa - 1 = 0

(2cosa + 1)(cosa - 1) = 0

cosa = 1 or cosa = -1/2

If cosa = 1, then a = 0.

If cosa = -1/2, then a = 2π/3 or 4π/3

Solutions in the interval [0, 2π): 0, 2π/3, 4π/3