Exercise 3.2: Curve plotting

Although the plot function is designed primarily for plotting standard xy graphs, it can be adapted for other kinds of plotting as well.

  1. a)  Make a plot of the so-called deltoid curve, which is defined parametrically by the equations, x = 2 cos θ + cos 2θ, y = 2 sin θ − sin 2θ, where 0 ≤ θ < 2π. Take a set of values of θ between zero and 2π and calculate x and y for each from the equations above, then plot y as a function of x.
  2. b)  Taking this approach a step further, one can make a polar plot r = f(θ) for some function f by calculating r for a range of values of θ and then converting r and θ to Cartesian coordinates using the standard equations x = r cos θ, y = r sin θ. Use this method to make a plot of the Galilean spiral, r=θ2 for 0 ≤ θ ≤ 10π.
  3. c)  Using the same method, make a polar plot of “Fey’s function”

r = e^{\cos{\theta}} - 2 \cos{4 \theta} + \sin^5{\frac{\theta}{12}}

in the range 0 ≤ θ ≤ 24π.