Question

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

Answer 1

Answer:

Step-by-step 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 $y = \frac {-(-13) \pm \sqrt{13^2 - 4*3*12} } {2*12} =\frac{ 13 \pm \sqrt{13^2-12^2}} {24} = \frac {13 \pm5 }{24}\\ y = \frac {18} {24} = \frac 34; y= \frac 8 {24} = 1/3$

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.