Am I correctly finding the polar graph of r = cos(4θ)?

Question

What I did was find an incriminator, so I set the inner to $π/2$.

$4θ = π/2$

$θ = π/8$

So the table goes:

$θ = 0, π/8, π/4, 3π/8, π/2, 5π/8$

and evaluating the functions those polar values I get the r’s to be:

$r = 1, 0, -1, 0, 1, 0$

So the pairs are:

$0,1$

$π/8,0 $

$π/4,-1 $

$3π/8,0 $

$π/2,1 $

$5π/8, 0$

When I graph these I am confused where $π/4$, $-1$ would go. Very unsure if I am doing ant of this right.

Please help

Thank you

Answer 1

First, when you naively get a negative radius, that indeed means going to $\theta+180^\circ$ and using the absolute value of $r$.

Next, I suggest for this curve you use smaller step sizes, perhaps $\frac{\pi}{16}$ or even $\frac{\pi}{24}$. The work involved is less than you think because by the time you get to $\pi/4$ you begin retracing curve segments you already have.