Question

8 cos^{2}x -10sinx-11=0

Answer 1

cos^{2}x = 1 - sin²x
8(1 - sin²x) - 10sin x - 11 = 0
8 - 8sin²x - 10sin x - 11 = 0
- 8sin²x - 10sin x - 3 = 0        D = 4    sin x₁ = -3/4
                                                          sin x₂ = -1/2
x₁ = Arc sin(-3/4) = kπ+(-1)^k*arc sin(-3/4) = kπ+(-1)^k*( -0,84806 )
x₂ = Arc sin(-1/2) = kπ+(-1)^k*arc sin(-1/2) = kπ+(-1)^k*( -π/6 ).