Graphing Polar Equations

Pre-Calculus · Axiom Academy

EXAMPLE Graphing Polar Equations Build a table of values, watch out for negative radii, and identify the curve from its polar equation. Graph the polar equation . Build a table of values at the key angles, plot the points, and identify what kind of curve it produces. Nice work. A polar graph comes straight from a table of values — the only twist is reading a negative r as a point in the opposite direction. Sample, don't guess: evaluate r at and plot each pair. Negative radius: when r < 0 , plot the point a distance |r| in the direction opposite to . Here that simply retraces the same circle. Identify the family: is a circle of diameter a along the polar axis through the pole — so has diameter 3 . Other common polar curves you can read off the same way: Every one of these is just a table of values in disguise — recognizing the form tells you the shape before you plot a single point.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.