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Answer:
sin(θ) = (-7√65)/65
csc(θ) = (-√65)/7
Explanation:
The angle will have the given characteristics if its terminal ray passes through the 3rd-quadrant point (-4, -7). The distance from the origin to that point is ...
d = √((-4)² +(-7)²) = √65
The sine of the angle is the ratio of the y-coordinate to this value:
sin(θ) = -7/√65
sin(θ) = (-7√65)/65
The cosecant is the inverse of the sine
csc(θ) = (-√65)/7