SOLUTION: What is the exact value of cos(2theta) if tan(theta)=-3/4 and theta is in quadrant IV? I don't even know how to start this problem. Please show work, thanks

Question 830821: What is the exact value of cos(2theta) if tan(theta)=-3/4 and theta is in quadrant IV?
I don't even know how to start this problem. Please show work, thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What is the exact value of cos(2theta) if tan(theta)=-3/4 and theta is in quadrant IV?
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In QIV x is positive, y is negative and r is always positive in all quadrants.
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tan = y/x so y = -3 and x = 4
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Then r = sqrt(3^2+4^2] = 5
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sin = y/r = -3/5
cos = x/r = 4/5
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cos(2t) = cos^2(t)-sin^2(t) = (4/5)^2-(3/5)^2 = 7/25
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Cheers,
Stan H.
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