Precalculus
Polar Function Graphs worksheets
Build key-value tables, test symmetry, graph full polar curves, and identify circle, cardioid, limacon, rose, and lemniscate families.
Preview and downloadPrecalculus practice
Polar Coordinate Conversions worksheets
Convert exact points and bounded line or circle equations between rectangular and polar forms, including negative-radius equivalents.
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Give exact coordinates and angles, show quadrant reasoning, and record division restrictions.
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Customize this worksheetCoordinate descriptions carry restrictions
These sheets connect parametric, rectangular, polar, and vector representations while keeping the interval, orientation, quadrant, or algebraic restriction that makes each conversion equivalent.
Learning objective
What this activity builds
Use x=r cos(theta), y=r sin(theta), and r²=x²+y² while preserving restrictions introduced by algebra.
Worked example
Convert r=4cos(theta) to rectangular form.
x²+y²=4x.
Multiply by r, then replace r² with x²+y² and r cos(theta) with x.
Teaching notes
Make the practice count
- Determine the quadrant before naming theta.
- A negative radius reverses the ray by a half-turn.
- Do not divide by r or a trig function without checking lost points.
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Equation families apply only to equation conversion tasks. Point tasks use exact standard-angle coordinates; choose angle units and whether to include negative-radius equivalents.
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