Question 556880: I need help solving this equation: 4cos^2theta+4sintheta=5
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! 4cos^2theta+4sintheta=5
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For simplicity, let theta = x
If we use the identity, cos^2(x) = 1 - sin^2(x), we have a polynomial in sin(x):
4(1 - sin^2(x)) + 4sin(x) = 5
Divide through by 4, and simplifiy:
sin^2(x) - sin(x) + 1/4 = 0
This can be factored as:
(sin(x)-1/2)(sin(x)-1/2) = 0
So we need to find solutions of sin(x) = 1/2
In the first quadrant, this is x = 30 deg (pi/6)
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