SOLUTION: I am taking a trigonometry class right now and one of the equations I need help solving is: 2sin^2x+3sinx+1=0 From this equation I am required to use the quadratic formula,

Algebra ->  Trigonometry-basics -> SOLUTION: I am taking a trigonometry class right now and one of the equations I need help solving is: 2sin^2x+3sinx+1=0 From this equation I am required to use the quadratic formula,      Log On


   

Question 1000791: I am taking a trigonometry class right now and one of the equations I need help solving is:
2sin^2x+3sinx+1=0
From this equation I am required to use the quadratic formula, solve for all possible values of "x" and then find what angles "x" is on the unit circle.
I really am not sure how to solve this, I need some help. Thanks!
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hello,

introduce the new variable  y = sin(x).  You will get a quadratic equation for  y

2y%5E2+%2B+3y+%2B+1 = 0.

Solve it and find  y:   y = -1%2F2  and  y = -1.

Then determine x:

Case 1:   y = -1%2F2   --->   sin(x) = -1%2F2   --->   x = 210° + k*360°  and  x = 330° + k*360°.

Case 2:   y = -1   --->   sin(x) = -1   --->   x = 270° + k*360°

It is the standard way of solving non-linear equations.