Final answer:
The value of sin(θ₁), when cos(θ₁) = -13/30 and θ₁ is in quadrant III, is approximately √(731/900).
Step-by-step explanation:
In the given question, the angle Θ₁ is located in quadrant III and cos(Θ₁) = -13/30. We need to find the value of sin(Θ₁).
Since the angle is in quadrant III, the cosine function is negative. Using the identity sin²(Θ) + cos²(Θ) = 1, we can solve for sin(Θ) as follows:
sin(Θ) = +√(1 - cos²(Θ)) = +√(1 - ((-13/30)²)) = +√(1 - (169/900)) = +√((900 - 169)/900) = +√(731/900).
Therefore, the value of sin(Θ₁) is approximately +√(731/900).