# Finding exact values using the sum and difference identity

• Jul 3rd 2011, 12:48 AM
elieh
Finding exact values using the sum and difference identity
How can I find the exact value of $cos\frac{\pi}{12}$ using the sum and difference identity?

I'm guessing I'd have to split the fraction up, into 2 parts, but I'm not sure on how to proceed.

Help appreciated.
• Jul 3rd 2011, 01:53 AM
e^(i*pi)
Re: Finding exact values using the sum and difference identity
$\cos \left(\dfrac{\pi}{12}\right) = \cos \left(\dfrac{\pi}{4} - \dfrac{\pi}{6}\right)$
• Jul 3rd 2011, 03:50 AM
Soroban
Re: Finding exact values using the sum and difference identity

Another way . . .

$\frac{\pi}{12} \;=\;\frac{4\pi}{12} - \frac{3\pi}{12} \;=\;\frac{\pi}{3} - \frac{\pi}{4}$

• Jul 3rd 2011, 04:41 AM
waqarhaider
Re: Finding exact values using the sum and difference identity
you can also use the identity cos^2(x/2) = (1+cosx)/2

by taking (pie)/12 = [pie/6]/2
• Jul 3rd 2011, 07:38 AM
skeeter
Re: Finding exact values using the sum and difference identity
Quote:

Originally Posted by waqarhaider
you can also use the identity cos^2(x/2) = (1+cosx)/2

by taking (pie)/12 = [pie/6]/2

this is pi ...

http://www.mathsisfun.com/images/pi1.png

this is pie ...

http://www.bigoven.com/pics/rs/256/s...pkin-pie-2.jpg

... hungry?