Question

Use the given information to determine the exact trigonometric value.

Answer 1

A.)
`-(2√(6) )/(5)`

Explanation:

Answer 2

A

Explanation:

Use the main trigonometric equality:

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

Since
`\sin\theta=-(1)/(5),` you have that

`\cos^2\theta=1-\left(-(1)/(5)\right)^2=1-(1)/(25)=(24)/(25).`

You know that
`\pi<\theta<(3\pi)/(2),` thus
`\cos \theta<0`

and

`\cos\theta=-\sqrt{(24)/(25)}=-(2√(6))/(5).`