Homework Help: Cos(x): 8 in x's denominator

1. Mar 11, 2007

sony

I have (from a complex equation problem) found the following angles in the answers:

5PI/8, 9PI/8, 13PI/8, 17PI/8

In the same assignement I found sin(PI/8) = .5*sqrt(2-sqrt(2)) and I found the cos(PI/8) value by using standard trig. identities.

Is there an easy way to use this result to find the cos and sin of the angles stated? (The assignement tells us to use the answer we found from sin(PI/8))

I know I can find formulas for cos(5x) etc by using this method: http://library.thinkquest.org/C0110248/trigonometry/form3.htm

But that is going to take ages up to cos(17x) !

I think I've missed something here.

Thanks

Last edited by a moderator: Apr 22, 2017
2. Mar 11, 2007

arildno

Hmm.. 5/8-1/8=1/2, I think. And 17=16+1, if I'm not mistaken

3. Mar 11, 2007

sony

I'm not getting it... :P

4. Mar 11, 2007

arildno

$$\frac{17\pi}{8}=\frac{16\pi}{8}+\frac{1\pi}{8}=2\pi+\frac{\pi}{8}$$
For example

5. Mar 11, 2007

sony

ah, thanks I get it!