Graphing Polar Equations — Quiz

Question 7 • Precalculus

Which graph represents the polar curve r is equal to 3 minus 2 cosine theta ?

Answer

Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, pi). It has a convex at (0, 0).

Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, pi). It has an inner loop at (0, 0).

Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (6, StartFraction 3 pi Over 2 EndFraction). It has an inner loop at (0, 0).

Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, StartFraction 3 pi Over 2 EndFraction). It has an inner loop at (0, 0).

Explanation

For r = 3 − 2 cos θ, the radius is 1 when θ = 0 and 5 when θ = π. Since the minimum radius is positive, the curve never reaches the pole and has no inner loop. It is a dimpled limaçon, with its larger bulge toward the left; choice A is the graph without an inner loop.

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