SOLUTION: Find all values of theta in the interval 0°< theta <360° that satisfy the equation 2(sin theta +csc theta)=5

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Question 366464: Find all values of theta in the interval 0°< theta <360° that satisfy the equation 2(sin theta +csc theta)=5
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
sin+%28theta%29+%2B+csc+%28theta%29+=+5%2F2,
sin+%28theta%29+%2B1%2Fsin+%28theta%29+=+5%2F2,
%28%28sin+%28theta%29%29%5E2+%2B1%29%2Fsin%28theta%29+=+5%2F2,
2%28sin+%28theta%29%29%5E2+%2B2=+5sin%28theta%29+,
2%28sin+%28theta%29%29%5E2+-+5sin%28theta%29%2B2=+0,
%282sin%28theta%29-1%29%28sin%28theta%29-2%29+=+0. The first factor gives
2sin%28theta%29+=+1, or sin%28theta%29=1%2F2, giving theta = 30 or 150 degrees.
The second factor sin%28theta%29-2+=+0 does not give any solutions. (Why?)