if sin = -12/13 and x is in quadrant 3, what is tan2x?

Answer 1

Use the identity:

Since sin = -12/13 and since sine is opposite/hypotenuse, you can draw the following triangle:

The -5 comes from using the Pythagorean Theorem and applying the correct sign for Quadrant 3. Then tan(x) = 12/5 so tan²(x) = 144/25. Plugging those into the identity, you get:

tan(2x) = 2(12/5)/(1 - 144/25) = (24/5)/(-119/25) = -120/119