SOLUTION: Use algebra to find all angles theta between 0 and 2pie radians that satisfy the equation cos^2 x = sin x . Give your answer in radians.

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Question 504472: Use algebra to find all angles theta between 0 and 2pie radians that satisfy the equation cos^2 x = sin x . Give your answer in radians.
Answer by lwsshak3(11628) About Me  (Show Source):
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Use algebra to find all angles theta between 0 and 2pie radians that satisfy the equation cos^2 x = sin x . Give your answer in radians.
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cos^2 x = sin x
1-sin^2x=sinx
sin^2x+sinx-1=0
solve for sin x using following quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=1, c=-1
sinx=[-1±√(1-4*1*-1)]2*1
sinx=[-1±√5]/2
sinx=-1.618(reject, not in range)
or
sin x=.618
x=.67 and 2.48 radians in quadrants I and II where sin is positive.