Question

Solve each equation 12sin^2-13sinx+3=0​

Answer 1

Explanation:

(I assume it's
`12sin^2 x -13 sinx +3 = 0`)

Start by setting
`sinx = y` (or whichever letter you prefer). Your equation becomes
`12y^2 -13y +3 = 0` . Solving for y you get
`y = \frac {-(-13) \pm √(13^2 - 4*3*12) } {2*12} =\frac{ 13 \pm √(13^2-12^2)} {24} = \frac {13 \pm5 }{24}\\ y = \frac {18} {24} = \frac 34; y= \frac 8 {24} = 1/3`

But we're not done yet. Since we said
`sinx = y`, you need to solve both
`sinx = \frac 3 4` and
`sinx = \frac 1 3`, whose solutions are the inverse sine of said values, plus any number of complete rotations.