### Home > PC > Chapter 6 > Lesson 6.1.2 > Problem6-28

6-28.

Sylvie needs to solve $\cos x = −0.3$ on a math test. She knows that $\cos^{−1}$ is the inverse function for cosine, so she applies this function to both sides of the equation. This gives her $x = \cos^{−1}\left(− 0.3\right) ≈ 1.875$. But when her test is returned, she finds she earned only partial credit on the problem.

1. What is wrong with Sylvie’s method?

There are multiple solutions.

She needs to add multiples of $2π$, and include the negative values. $x = ±1.875 + 2πn$, where $n$ is an integer.