Polar plot $r = 1-2\cos(6\theta)$

Question

I have a task for school and we need to plot a polar function with MATLAB. The function is $r = 1-2\cos(6\theta)$.

I did this and I'm getting exactly the same as on Wolfram Alpha: https://www.wolframalpha.com/input/?i=polar+plot+r%3D1-2\cos(6theta)

I've used for $\theta$ a value between $0$ and $2\pi$. Now the question explitictly says we need to take into account the period and the domain of the function and we can use the logic function $r>0$ for this. But I didn't do this because I just took a value between $0$ and $2\pi$ for $\theta$. Am I doing something wrong here?

Thanks.

Answer 1

Matlab code:

 clear all 
 close all

 nPoints = 500; % Number of points for the plot 

 theta = linspace(0, 2*pi, nPoints); % Define the theta points

 r = 1 - 2*cos(6*theta); % Evaluate the radius for each theta

 x = r.*cos(theta); % Evaluate x for each theta
 y = r.*sin(theta); % Evaluate y for each theta

 plot(x,y) % Plot it!!!

Output: a nice flower!

Answer 2

As the function $r$ has period $\frac\pi3$, the curve is invariant by rotations of angle $\frac\pi 3$. Hence you have to draw a petal of the curve for $0\le\theta\le\frac\pi 3$, and deduce the five other petals by successive rotations.