Question

Help with Trigonometric identities

Answer 1

Answer:

Option 2

Step-by-step explanation:

Since theta is in the third quadrant, the sine of theta is negative.

By the Pythagorean identity,

$\sin \theta=-\frac{\sqrt{105}}{13}$

So, using the double angle formula for sine, we get that

$\sin 2\theta=\frac{16\sqrt{105}}{169}$