Did I sketch this polar curve correctly?

The formula is:

$r^2=-4 \sin(2\theta)$

I first made a reference chart in cartesian works with making use of values $\displaystyle \frac{\pi}{4}$, $\displaystyle \frac{\pi}{2}$, $\displaystyle \frac{3 \pi}{4}$, $\displaystyle \pi$. After that from that I created this:

Something appears off concerning that though. Should it be throughout the various other axis rather?

2022-06-07 14:37:08
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Answers: 2

Give the comment from Alon some factor to consider, though I had not been able to quickly remove your possible chart based upon that suggestion alone. Allow is think of the interval $\frac{\pi}{2}< \theta< \pi$. On that particular period, $\sin2\theta$ goes from $0$ to $-1$ to $0$, so $r^2=-4\sin2\theta$ goes from $0$ to $4$ to $0$, so $r$ goes from $0$ to $\pm 2$ to $0$ once more. Despite just how I analyze your chart, it claims that $r=\pm4$ at $\theta=\frac{\pi}{2}$ or $\theta=\frac{3\pi}{2}$ (or something along those lines).

2022-06-07 15:01:42

You can allow WolframAlpha plot this by revising it in Cartesian works with:

$$r^2=-4\sin2\theta=-2\sin\theta\cos\theta\;,$$ $$r^4=-2\sin\theta r\cos\theta r=-2xy\;.$$

Concerning your very own story: It appears it is not the axes you obtained blended, yet the sine and also cosine.

2022-06-07 15:00:45