# Thread: Find exact sine value

1. ## Find exact sine value

Originally Posted by Another user. Dont ask.
I need to find the exact value of sin(π/16) without using a calculator. I thought that to do this I have to use the formula: $\displaystyle sin(A+-B) = sinAcosB+-cosAsinB$ but I can't find the correct two angles that add up to π/16 from all the angles on the unit circle. Thanks for any help.
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2. You can use this: $\displaystyle \sin\frac{x}{2}=\sqrt{\frac{1-\cos x}{2}}$ and $\displaystyle \cos\frac{x}{2}=\sqrt{\frac{1+\cos x}{2}}$

$\displaystyle \sin\frac{\pi}{16}=\sqrt{\frac{1-\cos\frac{\pi}{8}}{2}}$

$\displaystyle \cos\frac{\pi}{8}=\sqrt{\frac{1+\cos\frac{\pi}{4}} {2}}$
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