Solve the equation given. Enter all solutions, in degrees, that lie in the interval [0∘,360∘). Do not enter the degree sign. If there are more than one angle, separate them by a comma. sinβ+1=2cos2β

Question

Solve the equation given.

Answer 1

sinβ + 1 = 2cos2β; sinβ + 1 = 2 - 4sin²β; 4sin²β + sinβ - 1 = 0; sinβ = (- 1 ± √17)/8

sinβ = (- 1 + √17)/8; sin^-1((- 1 + √17))/8) = 23°; or β = 180^° 23° = 157˜.

sinβ = (- 1 - ; √17)/8; β = 180° + sin^-1(1 + √17)/8) = 220˜ or β = 360° - sin°((1 + √17)/8) = 320°

Answer 2

sin β + 1 = 2(1 - sin² β)

Solve for β using Algebraic techniques.