SOLUTION: solve 2sin²x -5sinx-3=0

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Question 1105695: solve 2sin²x -5sinx-3=0
Answer by math_helper(2461) About Me  (Show Source):
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solve 2sin²x -5sinx-3=0
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I will solve +2sin%5E2%28x%29+-+5sin%28x%29+-+3+=+0 for +0%3C=+x+%3C=+2pi+


Let u = sin(x)
Then +2u%5E2+-+5u+-+3+=+0+
+%282u+%2B+1%29%28u+-+3%29+=+0+
+u=-1%2F2+ and +u=3+
Substitute back in for u:
+sin%28x%29+=+-1%2F2+ and +sin%28x%29+=+3+
+sin%28x%29+=+3+ has no solution, discard it.
sin%28x%29+=+-1%2F2+ —> ++x+=+-pi%2F6+ or +x+=+highlight%28%2811pi%29%2F6+%29+ (Q4 angle)
There is also a Q3 angle: +x+=+pi+%2B+abs%28%28-pi%2F6%29%29+=+highlight%28%287pi%29%2F6%29+ (Q3 angle)