Final answer:
The angle Θ lies in Quadrant IV because cosine is positive and sine is negative there. Using the Pythagorean identity, we calculate that sin Θ = -4/5. The correct answer to the question is (d) Quadrant IV, sin Θ = -4/5.
Step-by-step explanation:
The problem states that cos Θ = 3/5 and sin Θ < 0. Knowing that cosine is positive and sine is negative, we can identify that Θ is in the Quadrant IV, where cosine values are positive and sine values are negative. To find sin Θ, we apply the Pythagorean identity sin2 Θ + cos2 Θ = 1, giving us sin2 Θ = 1 - cos2 Θ, which translates to sin2 Θ = 1 - (3/5)2.
Calculating further, we have sin2 Θ = 1 - 9/25, which simplifies to sin2 Θ = 16/25. Taking the square root, we get sin Θ = ±4/5, but since we know that sin Θ is negative in the fourth quadrant, sin Θ = -4/5. Hence, the correct answer is (d) Quadrant IV, sin Θ = -4/5.