SOLUTION: Find sinalpha if tan(alpha/2)=1/root2

Question 520169: Find sinalpha if tan(alpha/2)=1/root2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find sin(alpha) if tan(alpha/2) = 1/sqrt(2)
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Since tan(alpha/2) = y/x = 1/sqrt(2),
y = 1 when x = sqrt(2)
So, r = sqrt[1^2+(sqrt(2))^2] = sqrt(1+2) = sqrt(3)
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Then sin(alpha/2) = y/r = 1/sqrt(3)
and cos(alpha/2) = x/r = sqrt(2)/sqrt(3) = (1/3)sqrt(6)
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Finally, sin(alpha) = sin(2(alpha/2)) = 2sin(alpha/2)*cos(alpha/2)
= 2
---
= (2sqrt(6)/(3*sqrt(3))
------
= (2/3)[sqrt(18)/3]
---
= (2/3)sqrt(2)
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Cheers,
Stan H.
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