Graphing Polar Equations — Quiz

Question 3 • Precalculus

Which graph represents the polar curve r is equal to 4 cosine 3 theta ?

Answer

Image with description On a polar coordinate plane, a rose curve has 3 petals. One petal goes to (4, 0), another to (4, StartFraction 2 pi Over 3), and another goes to (4, StartFraction 4 pi Over 3 EndFraction).

Image with description On a polar coordinate plane, a rose curve has 8 petals. The petals are not on the x- or y-axes.

Image with description On a polar coordinate plane, a rose curve has 8 petals. Four petals are on the x and y-axes.

Image with description On a polar coordinate plane, a rose curve has 3 petals. One petal goes to (4, StartFraction pi Over 6 EndFraction), another to (4, StartFraction 5 pi Over 6), and another goes to (4, StartFraction 3 pi Over 2 EndFraction).

Explanation

For a polar rose of the form r = a cos(nθ), an odd n gives n petals, so this curve has 3 petals. Petal tips occur when cos(3θ) = 1, which gives θ = 0, 2π/3, and 4π/3; at each tip, r = 4. Thus the graph with petals reaching (4, 0), (4, 2π/3), and (4, 4π/3) is the correct one.

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