Question

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Answer 1

B

using SOHCAHTOA

COS THETA WILL BE EQUALS TO ROOT 5/3 AND TAN THETA WILL BE EQUALS TO 2ROOT 5/3

Answer 2

B.

Explanation:

First, note that since
`sin(\theta)=2/3`, this means that the opposite side is 2, the hypotenuse is 3, and the last, adjacent side is
`\sqrt{5\\`.

Also note that we are told that
`sec(\theta)<0`. This means that
`\theta` cannot be in quadrants 1 nor 4 because (remember All Students Take Calculus?) in those quadrants cosine and secant are positive. Also, we know that sine is positive so we can conclude that
`\theta` is in the second quadrant.

In the second quadrant, sine is positive, cosine is negative, and tangent is negative. Now we can answer the question. We already know the side lengths: opposite=2, adjacent=
`-√(5)` (because it's in Quadrant II), and hypotenuse=3.

Therefore...

`cos(\theta)=-√(5) /3`

`tan(\theta)=2/(-√(5))=-(2√(5)/5)`