A laser rangefinder is locked on a comet approaching Earth. The distance, g(x), in kilometers, of the comet after x days, for x in the interval 0 to 36 days, is given by g(x) = 250,000csc((pi/36)x).
a. Graph g(x) on the interval [0,36].
b. Evaluate g(6) and enter the exact answer.
c. What is the minimum distance between the comet and the Earth? When does this occur? To which constant in the equation does this correspond?
d. Find and discuss the meaning of any vertical asymptotes on the interval [0,36].