# Trigonometric addtion/subtraction & half identity problem.

• Mar 1st 2010, 10:29 AM
F.A.S.T.
Trigonometric addtion/subtraction & half identity problem.
Sorry, this problem is killing me. Normally it would be easy, but I'm havein problems breaking the radian mesure 11pie/12. Here is the problem.

Using the radian mesure of 11pie/12, choose sine, cosine, or tangent and develop the exact value of that measure using the angle addition or subtraction identity and the half angle identity. Show the work below. The answers you come up with for both should be equal, even hough they may not be written in the same form.

Thank you!
• Mar 1st 2010, 10:49 AM
running-gag
Hi

You know the value for $\displaystyle \cos \left(\frac{\pi}{6}\right)$ and $\displaystyle \sin \left(\frac{\pi}{6}\right)$

Using $\displaystyle \cos(2a) = 2 \cos^2a-1 = 1 - 2 \sin^2a$ with $\displaystyle a = \frac{\pi}{12}$ will give you the exact values for $\displaystyle \cos \left(\frac{\pi}{12}\right)$ and $\displaystyle \sin \left(\frac{\pi}{12}\right)$

And $\displaystyle \cos \left(\frac{11\pi}{12}\right) = \cos \left(\pi-\frac{\pi}{12}\right) = -\cos \left(\frac{\pi}{12}\right)$

$\displaystyle \sin \left(\frac{11\pi}{12}\right) = \sin \left(\pi-\frac{\pi}{12}\right) = \sin \left(\frac{\pi}{12}\right)$
• Mar 1st 2010, 04:22 PM
F.A.S.T.
^Well that answer is good, how did you/do you get it into the from of: cos(x+y)=cosXcosY-sinXsinY?
I got the Half angle for cos.
The equation finishes like so:
http://i112.photobucket.com/albums/n...ob_21/Math.png
The two answers should be equal...
Sorry the first sin should be a cos...
• Mar 1st 2010, 05:07 PM
F.A.S.T.