SOLUTION: Find all solutions of the equation 3 sin^2 x - 7 sin x + 2 = 0 in the interval [0,2pi). I need help trying to figure this out.

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions of the equation 3 sin^2 x - 7 sin x + 2 = 0 in the interval [0,2pi). I need help trying to figure this out.      Log On


   

Question 928166: Find all solutions of the equation 3 sin^2 x - 7 sin x + 2 = 0 in the interval [0,2pi).
I need help trying to figure this out.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute,
u=sin%28x%29
.
.
3u%5E2-7x%2B2=0
%28u-2%29%283u-1%29=0
Two "u" solutions:
u-2=0
u=2
sin%28x%29=2
No solution since sin%28x%29%3C=1
.
.
.
3u-1=0
3u=1
u=1%2F3
sin%28x%29=1%2F3
x=19.5 and x=160.5 degrees