Graphs of the Other Trigonometric Functions · Exercise 56

A laser rangefinder is locked on a comet approaching Earth. The distance $g\left(x\right),$ in kilometers, of the comet after $x$ days, for $x$ in the interval 0 to 30 days, is given by $g\left(x\right)=250,000csc\left(\frac{\pi }{30}x\right).$

ⓐ Graph $g\left(x\right)$ on the interval $\left[0,30\right].$
ⓑ Evaluate $g\left(5\right)$ and interpret the information.
ⓒ What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond?
ⓓ Find and discuss the meaning of any vertical asymptotes.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §8.2 Graphs of the Other Trigonometric Functions · Exercise 56