### Home > PC > Chapter 6 > Lesson 6.1.2 > Problem6-26

6-26.

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?

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 $\cos x=\frac{1}{2}$.

$x=\frac{\pi}{3}+2\pi n$ 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?

Draw a unit circle and think!