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cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,-4*%pi,0.5*%pi], [v,0*%pi,1.97*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=1/cosh(u)*sin...

Calculate

cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,0,2*%pi], [v,-1,1], [grid,50,20],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=sinh(u);

Calculate

cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,-10,10], [v,0,2*%pi], [grid,100,20],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=1/cosh(u)*sin...

Calculate

cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,0,0.8], [v,-1*%pi,1*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=sinh(u);

Calculate

cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,-0.5*%pi,0], [v,0*%pi,1.95*%pi], [grid,100,50],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=1/cosh(u)*sin...

Calculate

cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,-1,10], [v,2*%pi,4*%pi], [grid,20,20],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=1/cosh(u)*sin...

Calculate

cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,-4*%pi,4*%pi], [v,1*%pi,2.9*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=1/cosh(u)*sin...

Calculate

cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,-1*%pi,0], [v,0*%pi,1.95*%pi], [grid,100,50],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=1/cosh(u)*sin...

Calculate

cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,-0.5*%pi,0.75*%pi], [v,0*%pi,1.95*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=1/cosh(u)*sin...

Calculate

cosh-plot3d-sin-sinh
plot3d([x(u,v),y(u,v),z(u,v)], [u,-1,1], [v,0,2*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);

x(u,v):=1/cosh(u)*cos...

y(u,v):=1/cosh(u)*sin...

z(u,v):=sinh(u);

Calculate

[cosh,plot3d,sin,sinh]

Run Example
(%i1)x(u,v):=1/cosh(u)*cos(v);
                                         1
(%o1)                      x(u, v) := ------- cos(v)
                                      cosh(u)
(%i2) y(u,v):=1/cosh(u)*sin(v);
                                         1
(%o2)                      y(u, v) := ------- sin(v)
                                      cosh(u)
(%i3) z(u,v):=1/cosh(u)*sinh(u);
                                        1
(%o3)                     z(u, v) := ------- sinh(u)
                                     cosh(u)
(%i4) plot3d([x(u,v),y(u,v),z(u,v)], [u,-4*%pi,1*%pi], [v,0*%pi,1.5*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);
plotplot3d([x(u,v),y(u,v),z(u,v)], [u,-4*%pi,1*%pi], [v,0*%pi,1.5*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);
Run Example
x(u,v):=1/cosh(u)*cos(v);
                                         1
(%o1)                      x(u, v) := ------- cos(v)
                                      cosh(u)
(%i2) y(u,v):=1/cosh(u)*sin(v);
                                         1
(%o2)                      y(u, v) := ------- sin(v)
                                      cosh(u)
(%i3) z(u,v):=1/cosh(u)*sinh(u);
                                        1
(%o3)                     z(u, v) := ------- sinh(u)
                                     cosh(u)
(%i4) plot3d([x(u,v),y(u,v),z(u,v)], [u,-0.5*%pi,1*%pi], [v,0*%pi,1.95*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);
plotplot3d([x(u,v),y(u,v),z(u,v)], [u,-0.5*%pi,1*%pi], [v,0*%pi,1.95*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);
Run Example
x(u,v):=1/cosh(u)*cos(v);
                                         1
(%o1)                      x(u, v) := ------- cos(v)
                                      cosh(u)
(%i2) y(u,v):=1/cosh(u)*sin(v);
                                         1
(%o2)                      y(u, v) := ------- sin(v)
                                      cosh(u)
(%i3) z(u,v):=1/cosh(u)*sinh(u);
                                        1
(%o3)                     z(u, v) := ------- sinh(u)
                                     cosh(u)
(%i4) plot3d([x(u,v),y(u,v),z(u,v)], [u,-0.5*%pi,0.5*%pi], [v,0*%pi,1.97*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);
plotplot3d([x(u,v),y(u,v),z(u,v)], [u,-0.5*%pi,0.5*%pi], [v,0*%pi,1.97*%pi], [grid,50,20],[palette,get_plot_option(palette,3)]);

Related Help

Help for Cosh

Help for Plot3d

Help for Sin

Help for Sinh