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 , producing curves such as rose curves, cardioids, limaçons, and circles in the polar plane.
As the angle sweeps around, the distance 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.
Showing a random 20 of 50 problems.
Example 1
mediumConvert the polar curve to rectangular form.
Example 2
mediumIdentify the curve .
Example 3
hardFind all polar-coordinate intersection points of and for .
Example 4
hardFind the slope of the tangent to at .
Example 5
easyWhat curve is ?
Example 6
easyHow many petals does have?
Example 7
mediumFind the slope of the tangent to at .
Example 8
mediumClassify .
Example 9
easyDescribe the graph of in polar coordinates.
Example 10
easyHow many petals does have?
Example 11
challengeFor the rose , find the area of one petal using .
Example 12
easyWhat curve is represented by ?
Example 13
easyWhat type of curve is ?
Example 14
easyIdentify as a cardioid, dimpled limaçon, convex limaçon, or limaçon with inner loop.
Example 15
mediumIdentify whether the graph of has any symmetry about the line .
Example 16
mediumHow many petals does have, and how long is each?
Example 17
mediumHow many petals does have?
Example 18
hardFind the arc length of the cardioid .
Example 19
easyWhat curve is ?
Example 20
challengeFind the area inside the cardioid but outside the circle .