When James solved $\cos x=\frac{1}{2}$, he got $x = \cos^{-1}\left(\frac{1}{2}\right)$. His calculator told him that x = 1.047. Verify that this corresponds to the exact solution $\frac{\pi}{3}$. 

1. We also know $\frac{5\pi}{3}$ is a solution to $x = \cos^{-1}\left(\frac{1}{2}\right)$, but the calculator doesn’t give that answer. Why?

   Answer (a):

   There are an infinite number of solutions. The calculator chooses the solution that is in the domain of the function's inverse.

2. Write the complete solution to $\cos x=\frac{1}{2}$.

   Answer (b):

   $x=\frac{\pi}{3}+2\pi n$ or $x=\frac{5\pi}{3}+2\pi n$

3. Can you get the complete solution entirely from a calculator? If not, what do you need to do to get the complete solution?  

   Answer (c):

   Draw a unit circle and think!