### using MuPAD to plot curves using parametric equations.

The following link provides help with using MuPAD to plot curves using parametric equations.

http://www.mathworks.com/help/symbolic/mupad_ref/plot-curve2d.html

- Use MuPAD to plot the following curves using parametric equations.

(a) Figure 10 on page 643 of the text.

(b) Figure 12 on page 643 of the text.

(c) Figure IV from problem #28 on page 646 of the text (you must find the correct set

of parametric equations from the six listed in the problem).

(d) The cycloid curve produced from a wheel of radius 5 units rolling three complete

revolutions.

Hint: Use the Mesh option if the curve does not look smooth at first. The default value

is Mesh=121 (i.e. MuPAD plots 121 points of the curve in the parameter range that you

specify, so increasing this number may be necessary to produce a smooth curve).

- For the cycloid curve from problem 1 part d, use MuPAD to calculate the slope of the line

tangent to that curve when θ =

2π3

. Then plot the tangent line on the same graph as the

cycloid curve.

Hint: while plot::Curve2d is used to generate plot objects using parametric equations,

for Cartesian equations plot::Function2d is used for creating a plot object.

e.g. plot1:=plot::Function2d(2*(x-4)+1,x=0..10) would create a plot object for a

straight line and assign it to the variable plot1. Use the display command to plot

multiple plot objects on the same set of axes (e.g. display(plot1,plot2,. . .)).

- Use MuPAD to produce the graphs of the following curves that are defined using polar

coordinates. The handout from class should serve as a guide for producing polar plots.

(a) Figure 17 on page 665.

(b) Figure I from problem #54 on page 667 of the text (you must find the correct polar

equation from the six listed in the problem)