Given tan theta=-3/4 and theta in quadrant 2 find sin2 theta

Question

jusy need simplified

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the exact value of sin2θ from tanθ = -3/4. Then, as we yield the triangle and compute the pythagorean theorem, we get

sinθ = -3/5 and

cosθ = 4/5

We must also highlight the fact that sin2θ = 2cosθsinθ such that

sin2θ = 2(4/5)(-3/5)

sin2θ = -24/25

I hope this helped!