$\displaystyle Cos\left(\frac{\pi}{3} + x\right) = \frac{cos(x) - \sqrt{3}\;sin(x)}{2}$
This doesn't answer a lot of "why" question, but does give the information in an organized page.
The teacher may/may not be bad, but I'm betting the text is better than you are giving it credit for. (Probably the teacher as well.) Have you tried talking to your teacher about getting extra help?
-Dan
No this teacher is bad. he talks to himself the entire time and lets us out early 1 hour each class. I understand what plato is saying about the identity but i dont get where the 2 in the denominator comes from and as well as where do you go from there.
I get how $\displaystyle Cos\left(\frac{\pi}{3} + x\right)$ becomes $\displaystyle Cos\left(\frac{\pi}{3}\right)\;Cos(x) - Sin\left(\frac{\pi}{3}\right)\;Sin(x)$
But I dont get how that becomes $\displaystyle \frac{1}{2}\;Cos(x) - \frac{1}{2}\;\sqrt{3}\;Sin(x)$
I know that the Cosine of $\displaystyle \frac{\pi}{3} = .5$ but the sine of $\displaystyle \frac{\pi}{3}$ doesnt equal $\displaystyle .5$
Is this making sense?