how do you find the cos 17pi/6 in terms of pi

My answer is the same as Azis's.  Just the presentation is a little different.  

$$cos\frac{17\pi}{6}\\\\
=cos\left(\frac{12\pi}{6}+\frac{5\pi}{6}\right)\\\\
=cos\left(2\pi+\frac{5\pi}{6}\right)\\\\
=cos\left(\frac{5\pi}{6}\right)\\\\
\mbox{This is in the second quad - cos is negative}\\\\
=-cos\left(\frac{\pi}{6}\right)\\\\
=\frac{-\sqrt3}{2}$$

cos(17pi/6)

We know that pi/6 = 30 degrees, so 17pi/6 must be 30*17 = 510 degrees.

Also, note that pi = 180 degrees which means 2pi = 360 degrees.

Now, 510 - 360 degrees = 150 degrees, which means we have made a full 2pi revolution and are left with 150 degrees --> which is pi/6*5 [30 degrees*5 = 150 degrees] --> 5pi/6.

Now, cos(5pi/6) can be evaluated as 150 degrees or the 2nd quadrant with a negative x value since pi/6 is positive sqrt3/2 and lies in the 1st quadrant.

Therefore, we have cos(5pi/6) = -sqrt(3)/2.