<aside> 🐡 Given a point $P$ in the plane with Cartesian coordiates $(x,y)$and polar coordinates $(r, \theta)$: $x = r\cos \theta$ and $y = r\sin \theta$ $r^2=x^2+y^2$ and $\tan \theta = \frac{y}{x}$

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Plotting a Curve in Polar Coordinates

1. Create a table with $\theta$ and $r$
   1. Create list of values for $\theta$
   2. Use $\theta$ to calculate each value for $r$
2. Plot each ordered pair $(r, \theta)$ on the coordinate axes
3. Connect the points and look for a pattern
   1. Look for symmetry!

Symmetry of Polar Equations

1. If $f(\theta) = f(-\theta)$
   1. Symmetric about “x-axis”
2. If $f(\pi -\theta) = f(\theta)$
   1. Symmetric about “y-axis”
3. If $f(\theta + \pi) = -f(\theta)$
   1. Symmetric about origin

Common Curves