how do i get the exact value of cos(13pi/3)

13 pi /3 is equal to  4 1/3  pi    which is the same as  pi/3    (every 2 pi is a complete circle and gets you back to your starting point) 

cos pi/3  = cos 60 = 1/2

how do i get the exact value of cos(13pi/3)

\(cos\frac{13\pi}{3}\\ =cos(\frac{12\pi}{3}+\frac{\pi}{3})\\ =cos(4\pi+\frac{\pi}{3})\\ =cos(2\pi+2\pi+\frac{\pi}{3})\\ =cos(\frac{\pi}{3})\\ =cos60^\circ\)

Now you can read cos 60 straight off this triangle :)