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

1. $x=\frac{5\pi}{3}$ is a solution to $\cos(x)=\frac{1}{2}$, but James’ calculator did not 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. Solve $\cos(x)=\frac{1}{2}$ for all real $x$.

   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, or do you have to draw and think?  

   Answer (c):

   No, a calculator only gives one possible solution.