Find the solutions to 5 cos2 x 9sin x 3 on 0 2 piSolution 5

Find the solutions to -5 cos^2 x +9sin x = -3 on [0, 2 pi]

Solution

- 5cos^2x + 9sin x = -3

adding 3 on both sides

-5cos^2 x + 9sin x + 3 = 0

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

-5(1-sin^2 x ) + 9sin x + 3=0

-5 - 5sin^2 x + 9sin x + 3 = 0

-5sin^2 x + 9sin x - 2 = 0

on solving we get

sin x = 1/5 , sin x = -2

discarding sin x = -2

sin x = 1/5

x = sin^-1 ( 1/5)

x = .20136

x = pi - .20136