Question

Use the given information to determine the exact trigonometric value.

Answer 1

Answer:

A

Step-by-step explanation:

Use the main trigonometric equality:

$\cos ^2\theta+\sin^2\theta=1.$

Since $\sin\theta=-\dfrac{1}{5},$ you have that

$\cos^2\theta=1-\left(-\dfrac{1}{5}\right)^2=1-\dfrac{1}{25}=\dfrac{24}{25}.$

You know that $\pi$ thus $\cos \theta$

and

$\cos\theta=-\sqrt{\dfrac{24}{25}}=-\dfrac{2\sqrt{6}}{5}.$