SOLUTION: Solve the equation: {{{6sin^2(theta) + 5 sin (theta) = 6}}} Find all solutions on [0,2π). Round your solutions to the nearest tenth of a degree if necessary.

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation: {{{6sin^2(theta) + 5 sin (theta) = 6}}} Find all solutions on [0,2π). Round your solutions to the nearest tenth of a degree if necessary.      Log On


   

Question 929303: Solve the equation:
6sin%5E2%28theta%29+%2B+5+sin+%28theta%29+=+6
Find all solutions on [0,2π). Round your solutions to the nearest tenth of a degree if necessary.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute u=sin%28theta%29
6u%5E2%2B5u=6
6u%5E2%2B5u-6=0
%282u%2B3%29%283u-2%29=0
Two "u" solutions:
2u%2B3=0
2u=-3
u=-3%2F2
sin%28theta%29=-3%2F2
No solution since abs%28sin%28theta%29%29%3C=1
3u-2=0
3u=2
u=2%2F3
sin%28theta%29=2%2F3
theta=41.8 and theta=138.2