SOLUTION: if sinx= 3/5 on the interval(pi/2,pi), find the eact value of tan2x

Question 851698: if sinx= 3/5 on the interval(pi/2,pi), find the eact value of tan2x
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
if sinx= 3/5 on the interval(pi/2,pi), find the exact value of tan(2x)
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tan(2x) = [2tan(x)]/[1-tan^2(x)]
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Since sin(x) = 3/5, cos(x) = sqrt(5^2-3^2)/5 = sqrt(16)/5 = 4/5
Then tan(x) = sin(x)/cos(x) = 4/3
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Therefore: tan(2x) = [2(4/3)]/(1-(4/3)^2] = (8/3)/(-7/9) = -16/7
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Cheers,
Stan H.
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