SOLUTION: What is the exact value of sine of 13pie/12 ?

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Question 738265: What is the exact value of sine of 13pie/12 ?
Answer by lwsshak3(11628) About Me  (Show Source):
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What is the exact value of sine of 13pie/12 ?
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sin%2813pi%2F12%29=sin%28pi%2Bpi%2F12%29=-sin%28pi%2F12%29 (in Q3 where sin <0)
Use sin half-angle formula to solve: sin%28s%2F2%29=sqrt%28%281-cos%28s%29%29%2F2%29%29
sin(π/12)=sin((π/6)/2)
=±√(1-cos(π/6)/2)
=-√(1-(√3/2)/2)
=-√(2-√3/4)
=-√(2-√3)/2
Check with calculator:
sin(13π/12)≈-0.2588..
-√(2-√3)/2≈-0.2588..