how to solve trig equation

Question

3sin(α)+36sin^2(α)−3=0

Find all solutions to the equation below in the interval [0,2π)

Give all answers as decimals rounded to 3 places

Answer 1

36sin²a + 3sina - 3 = 0

Divide both sides by 3 to get 12sin²a + sina - 1 = 0

(3sina + 1)(4sina - 1) = 0

sina = 1/4 or -1/3

If sina = 1/4, then a = Sin^-1(1/4) or π - Sin^-1(1/4) = 0.253 or 2.889

If sina = -1/3, then a = π + Sin^-1(1/3) or 2π - Sin^-1(1/3) = 3.481 or 5.943

Answer 2

I will make an assumption (that William W. did not want to do), namely the the second terms is sin²a.

Dividing by 3 and rearranging terms gives

12sin²a + sin a -1 = 0

This is a quadratic equation in sin x which has roots 1/4 and -1/3.

You are therefore looking at arcsin x...but I suggest you graph this equation to make sure you get the correct answers.