Find sin theta if tan theta = sqrt3 / 3, and falls in quadrant 2

Question

Answer choices:

A) sin theta = -1/2

B) sin theta = 1/2

C) sin theta = sqrt3/2

D) sin theta = - sqrt3/2

Answer 1

If theta is in Q2, I'll assume you mean that tan theta = -sqrt(3)/3 since tan theta is negative if theta is in Q2.

Also, since theta is in Q2, sin theta must be > 0.

Imagine a right triangle where the side opposite theta is sqrt(3) and the side adjacent to theta is -3.

Use the pythagorean theorem to find the hypotenuse.

Once you know the hypotenuse, sin theta = sqrt(3) / hypotenuse.