Plotting in Matlab: w vs z in (-1,1) Domain

[lee403]

Homework Statement

(In Matlab) The variables w and z are related by w=cos(n*acos(z)) and z=cos(acos(w)/n) for n = 1,2,3,4 plot w vs z over domain (-1,1).

Homework Equations

w=cos(n*acos(z))
z=cos(acos(w)/n)

The Attempt at a Solution

First I tried to substitute z into w and thought since I have a function which calls itself I'd use a recursive function but I don't have the initial conditions. Then I thought that since the domain is (-1,1) and z would be plotted on that axis I could make z equal to an array with endpoints -1 and 1 and then plug that array in for w. Then I'd simply plot(z, w). The coding part is not difficult it's just the thought process behind it.

 

[RUber]

Normally, if you are asked to plot w vs. z over (-1, 1), you let one variable (say z) range from -1 to 1, and plot the other (w) as your dependent variable. In this case, I would try both ways.
Overlaying the two plots should show where both relations can be true at the same time.