Let's draw a picture of our problem:
The trigonometric value function of the angle beta will have the same value of the trigonometric value function of theta. Then, in order to find the cosine of beta, we can use the following right triangle
Therefore,
[tex]\cos \beta=\cos \theta=\frac{-4}{\sqrt[]{61}}[/tex]
or equivalently
[tex]\cos \beta=\frac{-4}{61}\sqrt[]{61}[/tex]
Therefore, the answer is correct.
