SOLUTION: Solve 8cos^2(x)-6sin(x)-9 = 0 for all solutions 0 <= x < 2pi

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Question 799270: Solve 8cos^2(x)-6sin(x)-9 = 0 for all solutions 0 <= x < 2pi
Answer by lwsshak3(11628) About Me  (Show Source):
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Solve 8cos^2(x)-6sin(x)-9 = 0 for all solutions 0 <= x < 2pi
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8cos^2(x)-6sin(x)-9 = 0
8(1-sin^2(x))-6sin(x)-9=0
8-8sin^2(x)-6sin(x)-9=0
8sin^2(x)+6sin(x)+1=0
solve for sin(x) using quadratic formula:
sin%28x%29+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=8, b=6, c=1
ans:
x=-0.5
sin(x)=-0.5
x=7π/6,11π/6(in quadrants III and IV where sin<0)
or
x=-0.25
sin(x)=-0.25
x≈3.3942,6.0305(in quadrants III and IV where sin<0)