Practice Polar Graphs in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Graphs of equations in the form r = f(\theta), producing curves such as rose curves, cardioids, limaçons, and circles in the polar plane.
As the angle \theta sweeps around, the distance r changes according to the equation, tracing out a curve. Think of it like a radar sweep where the blip's distance from the center varies with direction. This creates curves with stunning symmetry that would require complex implicit equations in Cartesian coordinates.
Example 1
easyDescribe the graph of r = 3 in polar coordinates.
Example 2
mediumIdentify the type of polar curve r = 2 + 2\cos\theta and find key features.
Example 3
mediumHow many petals does the rose curve r = 3\sin(4\theta) have?
Example 4
hardFind the area enclosed by one petal of the rose curve r = 4\cos(3\theta).