sin2𝜃, Pls read the description I am lost.

Question

1. Find the exact value of the following expression given that tan𝜃 =−2 and 90°<𝜃 <180°. Show all logic for your choices, including pictures of the quadrant to derive signs and a triangle to derive trigonometric values.

sin2𝜃

Pls help girl I am so confused.

Answer 1

If tan = -2 in quadrant 2, let y = 2 and x = -1. Then, r = √5. Thus, sinθ =y/r = 2/√5 and cosθ =x/r = -1/√5.

Then, sin2θ = 2sinθcosθ = 2(2/√5)(-1/√5) = -4/5