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.

Standing on the shore of a lake, a fisherman sights a boat far in the distance to his left. Let x, measured in radians, be the angle formed by the line of sight to the ship and a line due north from his position. Assume due north is 0 and x is measured negative to the left and positive to the right. (See Figure 19.) The boat travels from due west to due east and, ignoring the curvature of the Earth, the distance d(x), in kilometers, from the fisherman to the boat is given by the function d(x) = 1.5sec(x).

a. What is a reasonable domain for d(x)?

b. Graph d(x) on this domain.

c. Find and discuss the meaning of any vertical asymptotes on the graph of d(x).

d. Calculate and interpret d (−π/3) .Round to the second decimal place.

e. Calculate and interpret d (π/6) .Round to the second decimal place.

f. What is the minimum distance between the fisherman and the boat? When does this occur?

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W * E SO Figure 19