Exercises 3843 are made feasible through the use of appropriate software for graphing in

Chapter 1, Problem 42

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Exercises 3843 are made feasible through the use of appropriate software for graphing in polar, cylindrical, and spherical coordinates. (Note: When using software for graphing in spherical coordinates, be sure to check the definitions that are used for the angles and .) a y x b B P c Figure 1.124 The configuration for finding parametric equations for epitrochoids.(a) Graph the curve in R2 whose polar equation is r = 1 + sin 2 . (This curve is known as a nephroid, meaning kidney shaped.) (b) Graph the surface in R3 whose cylindrical equation is r = 1 + sin 2 . (c) Graph the surface in R3 whose spherical equation is = 1 + sin 2 . (d) Graph the surface in R3 whose spherical equation is = 1 + sin 2 .