SOLUTION: sin(x)=8/17 and pi/2 less than x less than pi. Find the exact value of tan(2x)

Question 959057: sin(x)=8/17 and pi/2 less than x less than pi. Find the exact value of tan(2x)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
sin(x)=8/17 and pi/2 less than x less than pi.
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x is in QII where x is cos(x) is negative.
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cos(x) = -sqrt[17^2-8^2]/17 = -15/17
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tan(x) = sin(x)/cos(x) = (8/17)/(-15/17) = -8/15
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Find the exact value of tan(2x)
tan(2x) = [2tan(x)]/[1-tan^2(x)] = [2(-8/15)]/[1-(64/225)]
= (-16/15)/[(225-64)/225]
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= (-16/15)/(161/225)
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= (-16*15)/161 = -1.49
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Cheers,
Stan H.
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