739 7.5 Inverse Circular Functions 109. Communications Satellite Coverage The figure shows a stationary communications satellite positioned 20,000 mi above the equator. What percent, to the nearest tenth, of the equator can be seen from the satellite? The diameter of Earth is 7927 mi at the equator. u 110. Oil in a Storage Tank The level of oil in a storage tank buried in the ground can be found in much the same way as a dipstick is used to determine the oil level in an automobile crankcase. Suppose the ends of the cylindrical storage tank in the figure are circles of radius 3 ft and the cylinder is 20 ft long. Determine the volume of oil in the tank to the nearest cubic foot if the rod shows a depth of 2 ft. (Hint: The volume will be 20 times the area of the shaded segment of the circle shown in the figure on the right.) 2 ft 3 ft Relating Concepts For individual or collaborative investigation (Exercises 111 – 114)* 111. Consider the function ƒ1x2 = 3x - 2 and its inverse ƒ -11x2 = 1 3 x + 2 3 . Simplify ƒ1ƒ -11x22 and ƒ -11ƒ1x22. What do you notice in each case? 112. Now consider the general linear functions ƒ1x2 = ax + b and ƒ -11x2 = 1 a x - b a , for a≠0. Simplify ƒ1ƒ -11x22 and ƒ -11ƒ1x22. What do you notice in each case? What is the graph in each case? 113. Use a graphing calculator to graph y = tan1tan-1 x2 in the standard viewing window, using radian mode. How does this compare to the graph you described in Exercise 112? 114. Use a graphing calculator to graph y = tan-11tan x2 in the standard viewing window, using radian and dot modes. Why does this graph not agree with the graph you found in Exercise 113? * The authors wish to thank Carol Walker of Hinds Community College for making a suggestion on which these exercises are based.
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