Additional Features of the plot command

The plot command has sevaral options that allow you to
create many types of graphs:
> plot({x^2, 2*x +5}, x=-10..10);

Parametric Form

You can graph curves expressed in parametric form. For example, the two equations
         x(t)= t-1   and  y(t)=t^2
gives the x and y coordinates of a parabolic curve based on a parameter t. If you solve these
two functional equations for y in terms of x by eliminating the parameter t, you will find that
   y=(x+1)^2.

1. Use the plot command with special grouping symbols,[ ], to graph the parametric curve just defined:
> plot([t-1, t^2, t=-2..2]);



> plot([t-1, t^2, t=-2..2], -5..5,-2..10);

Cycloid:
> plot([t-sin(t), 1-cos(t), t=0..4*Pi]);

Polar Form

The parametric graphing feature allows you  graph functions in polar coordinates:
> plot([sin(t),t, t=0..Pi], coords=polar);

> plot([sin(t),t, t=0..Pi], -3..3, -2..2, coords=polar);

Cardioid:
> plot([1 + cos(t), t, t=0..2*Pi], -3..3, -2..2, coords=polar);

> plot([1 + sin(t), t, t=0..2*Pi], -3..3, -2..2, coords=polar);

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