SOLUTION: How do I solve tan(theta)

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Question 655661: How do I solve tan(theta) - sin(theta) = 1/12 ?
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
How do I solve tan(theta) - sin(theta) = 1/12 ?
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tan - sin = 1/12
12tan - 12sin = 1
12sin/cos - 12sin = 1
12sin(1/cos - 1) = 1
12sin((1 - cos)/cos) = 1
12sin(1 - cos) = cos
12(1 - cos) = cos/sin
144(1 - 2cos + cos^2) = cos^2/sin^2 = cos^2/(1 - cos^2)
144(cos^2 - 2cos + 1)*(1 - cos^2) = cos^2
144(-cos^4 + 2cos^3 - 2cos + 1) = cos^2
-144cos^4 + 288cos^3 - cos^2 - 288cos + 144 = 0
144cos^4 - 288cos^3 + cos^2 + 288cos - 144 = 0
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Using graphical methods:
cos = -1
--> theta = pi radians, but tan(pi) - sin(pi) = 0
& cos =~ 0.8597282
--> theta =~ 30.71392 degs

SOLUTION: How do I solve tan(theta) - sin(theta) = 1/12 ?