Learn Construct complete noncircle polar curves, restrict their traces, and distinguish signed radius from distance and interpolation evidence without calculus.
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Curve construction must preserve the sign before converting to Cartesian coordinates.
The point lies opposite the terminal ray of its angle. Use x=r cos θ and y=r sin θ; the distance from the origin is |r|. For example, r=−1 at θ=π gives (1,0), at distance 1.
The two quantities can move in opposite directions when the radius is negative.
No. As r decreases from −1 to −2, distance increases from 1 to 2. Keep the angle interval and the scalar quantity explicit; neither change alone measures Cartesian travel length.
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Polar curve evidence: mixed practice
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Trace noncircle polar curves with exact sign intervals and meaningful angular restrictions.
6 practice tasks.
Prove distance intervals and use a polar table without inventing between-point accuracy.
6 practice tasks.