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Discover the Path to Mathematical Mastery
An Education That Counts
Common polar graphs. Quiz yourself to see if you know the general shapes for the given polar curve. Hover the mouse cursor over the plot to reveal the plot along with its trajectory. [Refresh your browser to reset the animation.]
| Polar to Rectangular | |
| \(x=r\texttt{cos}(\theta)\) | \(y=r\texttt{sin}(\theta)\) |
| Rectangular to Polar | |
| \(\displaystyle\frac{y}{x}=\texttt{tan}(\theta)\) | \(x^2+y^2=r^2\) |
Circle: \(r=a\)
\(0\leq\theta\leq2\pi\)
Circle: \(r=2a\texttt{cos}(\theta)\)
\(0\leq\theta\leq\pi\)
Circle: \(r=2a\texttt{sin}(\theta)\)
\(0\leq\theta\leq\pi\)
Limacon: \(r=\frac{1}{2}+\texttt{cos}(\theta)\)
\(0\leq\theta\leq2\pi\)
Cardioid: \(r=1+\texttt{cos}(\theta)\)
\(0\leq\theta\leq2\pi\)
Limacon: \(r=\frac{5}{2}+\texttt{cos}(\theta)\)
\(0\leq\theta\leq2\pi\)
Rose: \(r=\texttt{sin}(2\theta)\)
\(0\leq\theta\leq2\pi\)
Rose: \(r=\texttt{sin}(3\theta)\)
\(0\leq\theta\leq\pi\)
Rose: \(r=\texttt{sin}(4\theta)\)
\(0\leq\theta\leq2\pi\)
Rose: \(r=\texttt{cos}(2\theta)\)
\(0\leq\theta\leq2\pi\)
Rose: \(r=\texttt{cos}(3\theta)\)
\(0\leq\theta\leq\pi\)
Rose: \(r=\texttt{cos}(4\theta)\)
\(0\leq\theta\leq2\pi\)
Lemniscates: \(r^2=\texttt{cos}(2\theta)\)
\(0\leq\theta\leq2\pi\)
Lemniscates: \(r^2=\texttt{sin}(2\theta)\)
\(0\leq\theta\leq\pi\)
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