Answer:
A
Step-by-step explanation:
Use the main trigonometric equality:
[tex]\cos ^2\theta+\sin^2\theta=1.[/tex]
Since [tex]\sin\theta=-\dfrac{1}{5},[/tex] you have that
[tex]\cos^2\theta=1-\left(-\dfrac{1}{5}\right)^2=1-\dfrac{1}{25}=\dfrac{24}{25}.[/tex]
You know that [tex]\pi<\theta<\dfrac{3\pi}{2},[/tex] thus [tex]\cos \theta<0[/tex]
and
[tex]\cos\theta=-\sqrt{\dfrac{24}{25}}=-\dfrac{2\sqrt{6}}{5}.[/tex]
