Using a inverse trig function find the solution of the equat

Using a inverse trig function, find the solution of the equation in the interval [-pi/2,pi/2]. 3sin^2x-8sinx+4=0

Solution

3 sin^2 x - 8 sin x + 4 = 0

let sin x = y

3y^2 - 8y + 4 = 0

factoring the equation

3y^2 - 6y - 2y + 4 = 0

3y ( y-2 ) - 2(y-2)

(3y-2)(y-2) = 0

y = 2/3 , y = 2

therefore. sin x = 2/3 , x= sin^-1 ( 2/3 ) , x = .7297

sin x = 2 , no solutions

therefore, solution is

x = .7297