Homework SourseDetermine all the solutions of the equation 3 sin2 x sin x
Determine all the solutions of the equation:
3 sin2 x + sin x - 1 = 0
Solution
3sin^2 x + sin x -1 = 0
let sin x = y
3 y^2 + y - 1 = 0
solving for y
y = ( -1 + - sqrt (1 + 4*3*1 ) / 6
y = ( -1 + sqrt 13 ) / 6 , ( -1 - sqrt 13 ) / 6
or sin x = ( -1 + sqrt 13 ) / 6 , ( -1 - sqrt 13 ) / 6
x = sin^-1 ( -1 + sqrt 13 ) / 6 + 2n pi , pi - sin^-1 ( -1 + sqrt 13 ) / 6 + 2n pi
x = sin^-1 ( -1 - sqrt 13 ) / 6 + 2 npi , pi + sin^-1 ( -1 - sqrt 13 ) / 6 + 2 npi
