Final answer:
To find sin 2θ when given tanθ and the quadrant of θ, first find the value of θ and then use the double angle identity for sine.
Step-by-step explanation:
Given that tanθ = -3/5 and θ is in quadrant II, we need to find sin 2θ.
First, let's find the value of θ. Since tanθ = -3/5, we can find tan⁻¹(-3/5) ≈ -31.8°. However, θ is in quadrant II, so the reference angle is 180° - 31.8° = 148.2°. Therefore, θ = 180° + 148.2° = 328.2°.
To find sin 2θ, we can use the double angle identity for sine: sin 2θ = 2sin θcos θ.
Substituting the value of θ, we get sin 2θ = 2sin(328.2°)cos(328.2°).