# Find exact sine value

• Apr 20th 2009, 02:06 AM
mr fantastic
Find exact sine value
Quote:

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: $sin(A+-B) = sinAcosB+-cosAsinB$ 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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• Apr 20th 2009, 02:16 AM
red_dog
You can use this: $\sin\frac{x}{2}=\sqrt{\frac{1-\cos x}{2}}$ and $\cos\frac{x}{2}=\sqrt{\frac{1+\cos x}{2}}$

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

$\cos\frac{\pi}{8}=\sqrt{\frac{1+\cos\frac{\pi}{4}} {2}}$
• Apr 20th 2009, 03:05 AM
mr fantastic