## anonymous one year ago How do I get -(1+sqrt(3))/(2 sqrt(2)) from cos(11/12 pi) using half/double angle identities?

1. anonymous

$\cos(\frac{11}{12}\pi) =>-\frac{1+\sqrt{3}}{2\sqrt{2}}$

2. campbell_st

well look at it like this $\cos(\frac{11\pi}{12}) = \cos(\frac{2\pi}{3} + \frac{\pi}{4})$

3. campbell_st

then you need $\cos(A +B) = \cos(A)\cos(B) - \sin(A)\sin(B)$

4. campbell_st

the sum of both angles are exact values.... just remember $\frac{2\pi}{3} ~is~2nd~quadrant$

5. anonymous

Well, ok. I was hoping not to have to use sum/difference formulas because they are longer than:$\cos(\frac{\theta}{2})=\sqrt{\frac{1+\cos(\theta)}{2}}$ But I guess I just have to not be lazy and evaluate more trig functions.

6. campbell_st

sum and difference are the easiest for this question $\cos(\frac{\pi}{4}) = \sin(\frac{\pi}{4}) = \frac{1}{\sqrt{2}}$ $\cos(\frac{2\pi}{3}) = - \frac{1}{2}~~~~\sin(\frac{2\pi}{3}) = \frac{\sqrt{3}}{2}$ now just multiply the fractions... with is certainly easier than the half angle formula or double angle formula

7. anonymous

That makes sense; a little bit of thinking ahead goes a long way.