SOLUTION: 2sin^2 theta plus 3sin theta = -1 Solve for the given domain: 0greater than or equal to theta greater than or equal to 2pi

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Question 1022987: 2sin^2 theta plus 3sin theta = -1
Solve for the given domain:
0greater than or equal to theta greater than or equal to 2pi

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
2sin^2 theta plus 3sin theta = -1
Solve for the given domain:
0greater than or equal to theta greater than or equal to 2pi
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2%2Asin%5E2%28theta%29+%2B+3%2Asin%28theta%29 = -1,

2%2Asin%5E2%28theta%29+%2B+3%2Asin%28theta%29+%2B+1 = 0.

Factor left side:

(2*sin(theta) + 1)*(sin(theta) + 1) = 0,   --->

2%2Asin%28theta%29+%2B+1 = 0  or  sin%28theta%29+%2B+1 = 0,  --->

sin%28theta%29 = -1%2F2  or  sin%28theta%29 = -1,  --->

Solutions:

1.    theta = 7%2Api%2F6  or  theta = 11%2Api%2F6

or

2.    theta = 3%2Api%2F2.