Final answer:
The value of csc θ for the point (-3, -2) on the terminal side of an angle in standard position is -√13/2.
Step-by-step explanation:
If the point (-3, -2) lies on the terminal side of an angle θ in standard position, to find the value of csc θ in simplified radical form, we can use the Pythagorean Theorem to find the hypotenuse of the right triangle formed by the points (0,0), (-3,0), and (-3, -2). The lengths of the triangle's sides are 3 (along the x-axis) and 2 (along the y-axis), so the hypotenuse r, which is also the radius in polar coordinates, is given by r = √((-3)^2 + (-2)^2) = √(9 + 4) = √13.
Since csc θ is the reciprocal of sin θ, and sin θ is equal to the y-coordinate of the point on a unit circle divided by the hypotenuse, we have sin θ = -2/√13. Therefore, csc θ = -1/sin θ = -√13/2.
The correct answer to the question is C) -√13/2.