SOLUTION: If tanx is 3/4, with the triangle in the third quadrant, what is sin(x/2)?

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Question 1013114: If tanx is 3/4, with the triangle in the third quadrant, what is sin(x/2)?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If tan(t) is 3/4, with the triangle in the third quadrant, what is sin(t/2)?
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sin(t/2) = sqrt[(1-cos(t))/2]
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If tan(t) = 3/4, y = -3 and x = -4, since t is in QIII.
Then r = sqrt(3^2+4^2) = sqrt[25] = 5
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So cos(t) = -4/5
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Ans: sin(t/2) = sqrt[(1+(4/5))/2] = sqrt[9/10] = 3/sqrt(10)
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Cheers,
Stan H.