SOLUTION: Find the solutions of the equation that are in the interval [0,2π). Please show steps (especially rearranging the equation to solve it. Thanks for helping me. I know the solu

Algebra ->  Geometry-proofs -> SOLUTION: Find the solutions of the equation that are in the interval [0,2π). Please show steps (especially rearranging the equation to solve it. Thanks for helping me. I know the solu      Log On


   

Question 148679: Find the solutions of the equation that are in the interval [0,2π). Please show steps (especially rearranging the equation to solve it. Thanks for helping me. I know the solutions are 11π/6, π/2 but I just can't
figure out how to isolate to get those solutions. Thanks again.

1) 1-sint=(√3)cost
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
1 - sin(t) = √3)cos(t)
1 - 2sin(t) + sin^2(t) = 3cos^2(t)
1 - 2sin(t) + sin^2(t) = 3(1 - sin^2(t))
1 - 2sin(t) + sin^2(t) = 3 - 3sin^2(t)
4sin^2(t) - 2sin(t) - 2 = 0
2sin^2(t) - sin(t) - 1 = 0
(2sin(t) + 1)(sin(t) - 1) = 0
2sin(t) + 1 = 0 and sin(t) - 1 = 0
sin(t) = -1/2 and sin(t) = 1