Final answer:
The point (-9, -40) lies on the terminal side of θ in standard position. The value of csc θ is 1.025.
Step-by-step explanation:
The point (-9, -40) lies on the terminal side of θ in standard position. To find csc θ, we need to determine the value of the reciprocal of the sine function.
Using the Pythagorean theorem, we can find the hypotenuse of the right triangle formed by the point and the origin. The distance between the point (-9, -40) and the origin (0, 0) can be found as:
distance = √((-9)^2 + (-40)^2) = √(81 + 1600) = √1681 = 41
The reciprocal of sine is cosecant (csc), so csc θ can be found as:
csc θ = 1/sin θ = hypotenuse/opposite = 41/40 = 1.025