SOLUTION: Use half-angle identity to find the exact value of sin((5π)/(12)).
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Question 366650: Use half-angle identity to find the exact value of sin((5π)/(12)).
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Half-angle formula for sin:
\ =\ \frac{1}{2}\left\[1\ -\ \cos(a)\right\])
Hence:
\ =\ \frac{1}{2}\left\[1\ -\ \cos\left(\frac{5\pi}{6}\right)\right\])
Looking at the unit circle:
we see that \ =\ -\frac{\sqrt{3}}{2})
So:
\ =\ \frac{1}{2}\left\[1\ +\ \frac{\sqrt{3}}{2}\right\])
\ =\ \frac{2\ +\ \sqrt{3}}{4})
Since sin is positive on )
and 
, take the positive root:
\ =\ \frac{\sqrt{2\ +\ \sqrt{3}}}{2})
John
My calculator said it, I believe it, that settles it
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