SOLUTION: how do i find all the intervals of x which satisfy 2cos2x = 5 -5sinx, in radians?

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Question 332270: how do i find all the intervals of x which satisfy 2cos2x = 5 -5sinx, in radians?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
how do i find all the intervals of x which satisfy 2cos2x = 5 -5sinx, in radians?

2%2ACos%282x%29+=+5+-5%2ASin%28x%29

Use the identity Cos%282theta%29=1-2Sin%5E2theta 

2%281-2%2ASin%5E2%282x%29%29+=+5+-5%2ASin%28x%29

2-4%2ASin%5E2%282x%29=5-5%2ASin%28x%29

-4%2ASin%5E2%282x%29%2B5%2ASin%28x%29-3=0

Multiply through by -1:

4%2ASin%5E2%282x%29-5%2ASin%28x%29%2B3=0

That is a quadratic in Sin%28x%29.  However

the discriminant is b%5E2-4ac=%28-5%29%5E2-4%284%29%283%29=25-48=-23

Since the discriminant is negative, the solutions to the quadratic are
imaginary.

Therefore there can be no real number solutions.

Edwin