Drawing $(x_n,y_n) = \left((1+\frac{1}{5}(-1)^n)\cos n\theta,(1+\frac{1}{5}(-1)^n)\sin n\theta\right)$

Question

I have a problem where I am given this function:

$$\begin{cases} x_n = (1+\frac{1}{5}(-1)^n)\cos n\theta \\ y_n = (1+\frac{1}{5}(-1)^n)\sin n\theta \end{cases}$$

if $\theta=\frac{\pi}{5}$ , how should I draw this function $p(x_n,y_n)$? thank you in advence

Answer 1

Since both $x_n$ and $y_n$ are periodic you only need to plot the first $10$ points $P(x_n,y_n)$.

Since $x_n^2 + y_n ^2= (1\pm 1/5)^2$ your points are alternatively on two circles of radii $6/5$ and $4/5$