Final answer:
The value of csc θ, where the point (6, -8) lies on the terminal side of an angle θ in standard position, is -1.25, calculated using the reciprocal of the sine function which is y/r.
Step-by-step explanation:
To find the value of csc θ when a point (6, -8) lies on the terminal side of an angle θ in standard position, we first need to determine the radius (r) of the circle that the point lies on. This is found by using the Pythagorean Theorem:
r = √(x² + y²) = √(6² + (-8)²) = √(36 + 64) = √100 = 10
Since csc θ is the reciprocal of sine, which is y/r for an angle in standard position, we get:
csc θ = 1/sin θ = r/y
For the given point, y = -8 and r = 10, thus:
csc θ = 10 / -8
Therefore, csc θ = -1.25.