Construct the surface given by

ρ = 1 + sin θ,  0 ≤ θ ≤ π,  0 ≤ φ ≤ π 

 in spherical coordinates.

 做法：

 > plot3d(1+sin(t),t=0..Pi,s=0..Pi,coords=spherical,
                scaling=constrained);

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     Construct the surface obtained by rotating the cardioid  about
 its axis by 180 degrees. In polar coordinates, the cardioid is
 given by

ρ = 1 + cos θ,  0 ≤ θ ≤ 2π.

 做法：

  > r := 1 + cos(t)
  > x:=r*cos(t);
  > rho:=r*sin(t);
  > y:=rho*cos(s);
                                                       > z:=rho*sin(s);
                                                       > plot3d([x,y,z],t=0..Pi,s=0..Pi,scaling=constrained,
                 grid=[25,25],lightmodel=light2);    

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Construct the surface obtained by rotating the curve given, in
 polar coordinates, by

ρ = 1 + cos 2θ,  0 ≤ θ ≤ π/2 

.about the y-axis.

 做法：

  > r:=1+cos(2*t);
  > rho:=r*cos(t);
  > y:=r*sin(t);
  > x:=rho*cos(s);
  > z:=rho*sin(s);
  > plot3d([x,y,z],t=0..Pi/2,s=0..Pi,scaling=constrained,grid=[25,25]);

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x = 3 cos θ - cos 3θ

y = 3 sin θ - sin 3θ

0 ≤ θ ≤ 2π.

 Construct the surface obtained by rotating the nephroid about
 the y-axis.

 做法：

  > n:=3;
  > r:=n*cos(t)-cos(n*t);
  > x:=r*cos(s);
  > y:=r*sin(s);
  > z:=n*sin(t)-sin(n*t);
  > plot3d([x,y,z],t=-Pi/2..Pi/2,s=0..Pi,scaling=constrained);