Answer:
Step-by-step explanation:
(I assume it's [tex]12sin^2 x -13 sinx +3 = 0[/tex])
Start by setting [tex] sinx = y [/tex] (or whichever letter you prefer). Your equation becomes [tex] 12y^2 -13y +3 = 0[/tex] . Solving for y you get [tex]y = \frac {-(-13) \pm \sqrt{13^2 - 4*3*12} } {2*12} =\frac{ 13 \pm \sqrt{13^2-12^2}} {24} = \frac {13 \pm5 }{24}\\ y = \frac {18} {24} = \frac 34; y= \frac 8 {24} = 1/3[/tex]
But we're not done yet. Since we said [tex] sinx = y [/tex], you need to solve both [tex] sinx = \frac 3 4 [/tex] and [tex] sinx = \frac 1 3 [/tex], whose solutions are the inverse sine of said values, plus any number of complete rotations.
