### Home > PC3 > Chapter 2 > Lesson 2.3.2 > Problem2-139

2-139.

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?

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 $x$

$x=\frac{\pi}{3}+2\pi n$ 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?

No, a calculator only gives one possible solution.