For the following exercises, use a graphing calculator to graph two periods of the given function. Note: most graphing calculators do not have a cosecant button; therefore, you will need to input csc x as 1/sin x.

A video camera is focused on a rocket on a launching pad 2 miles from the camera. The angle of elevation from the ground to the rocket after x seconds is π/120 x.

a. Write a function expressing the altitude h(x), in miles, of the rocket above the ground after x seconds. Ignore the curvature of the Earth.

b. Graph h(x) on the interval (0, 60).

c. Evaluate and interpret the values h(0) and h(30).

d. What happens to the values of h(x) as x approaches 60 seconds? Interpret the meaning of this in terms of the problem.