Question

I NEED HELP PLEASE HURRY, THANKS! :)

Answer 1

Answer:

B

using SOHCAHTOA

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

Answer 2

Answer:

B.

Step-by-step 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 $sec(\theta)$. 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=$-\sqrt{5}$ (because it's in Quadrant II), and hypotenuse=3.

Therefore...

$cos(\theta)=-\sqrt{5} /3$

$tan(\theta)=2/(-\sqrt{5})=-(2\sqrt{5}/5)$