Finding exact values using the sum and difference identity

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July 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.
July 3rd 2011, 01:53 AM
e^(i*pi)

Re: Finding exact values using the sum and difference identity

$\cos \left(\dfrac{\pi}{12}\right) = \cos \left(\dfrac{\pi}{4} - \dfrac{\pi}{6}\right)$
July 3rd 2011, 03:50 AM
Soroban

Re: Finding exact values using the sum and difference identity

Another way . . .

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

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