Exercises 38–43 are made feasible through the use of appropriate software for graphi...

Exercises 38–43 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 φ and θ .)

(a) Graph the curve in R² whose polar equation is r = sin 3θ.

(b) Graph the surface inR³ whose cylindrical equation is r = sin 3θ.

(c) Graph the surface in R³ whose spherical equation is ρ = sin 3φ.

(d) Graph the surface in R³ whose spherical equation is ρ = sin 3θ. Compare the results of this exercise with those of Exercise 40.