Question 1000322: Find the exact value of tangent of 2 theta given sine of theta = 3 over 5 and theta is between 0 and pi over 2.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the exact value of tangent of 2 theta given sine of theta = 3 over 5 and theta is between 0 and pi over 2.
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Note:: x and y are both positive in QI
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By definition, sin = y/r
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Since sin = 3/5, y = 3 and r = 5
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Then x = sqrt[5^2-3^2] = 4
So, tan(t) = y/x = 3/4
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Note:: tan(2t) = (2*tan(t))/(1-tan^2(t))
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Ans: [2(3/4)]/[1-(3/4)^2] = (3/2)/[1-9/16] = (3/2)*(16/7) = 24/7 = 3 3/7
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Cheers,
Stan H.
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