SOLUTION: solve 2sinx-4cosx=3

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Question 775020: solve 2sinx-4cosx=3
Answer by lwsshak3(11628) About Me  (Show Source):
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solve 2sinx-4cosx=3
2sin%28x%29-4cos%28x%29=3
2sin%28x%29-4sqrt%281-sin%5E2%28x%29%29=3
2sin%28x%29-3=4sqrt%281-sin%5E2%28x%29%29
square both sides
4sin%5E2%28x%29-12sin%28x%29%2B9=16%281-sin%5E2%28x%29%29
4sin%5E2%28x%29-12sin%28x%29%2B9=16-16sin%5E2%28x%29%29
20sin%5E2%28x%29-12sin%28x%29-7=0
solve for sin(x) using quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=20, b=-12, c=-7
sin(x)≈-0.3633
x≈201.30º and 338.30º
or
sin(x)≈0.9633
x≈74.43º and 105.57º