Solve the equation in the interval 0 2 Round to four decimal

Solve the equation in the interval [0, 2). Round to four decimal places.

15 sin^2 x 22 sin x + 8 = 0

Solution

15sin^2 x - 22 sin x + 8 = 0

sin x = y

equation becomes

15y^2 - 22y + 8 = 0

factoring the equation we get

( 5y - 4) ( 3 y - 2) =0

y = 4/5 , y = 2/3

or

sin x = 4/5 , sin x = 2/3

x = pi - sin^-1 (4/5) , x = sin^-1 (4/5)

x = pi - sin^-1 (2/3) , x = sin^-1 (2/3 )

solutions are

x = .9273 , x = pi - .9273

x = pi - .7297 , x = .7297