Graphing Polar Equations — Quiz

Question 8 • Precalculus

Which graph represents points on the polar curve r is equal to 6 cosine theta ?

Answer

Image with description On a polar coordinate plane, points are at (0, 0), (6, 0), (4, StartFraction pi Over 4 EndFraction), and (4, StartFraction 7 pi Over 4 EndFraction).

Image with description On a polar coordinate plane, points are at (0, 0), (6, StartFraction pi Over 2 EndFraction), (4.5, StartFraction pi Over 4 EndFraction), and (4.5, StartFraction 3 pi Over 4 EndFraction).

Image with description On a polar coordinate plane, points are at (0, 0), (6, StartFraction 3 pi Over 2 EndFraction), (4.5, StartFraction 5 pi Over 4 EndFraction), and (4.5, StartFraction 7 pi Over 4 EndFraction).

Image with description On a polar coordinate plane, points are at (0, 0), (6, pi), (4.5, StartFraction 5 pi Over 4 EndFraction), and (4.5, StartFraction 3 pi Over 4 EndFraction).

Explanation

For θ = 0, the equation gives r = 6 cos(0) = 6, matching the point (6, 0) in choice D. For θ = π/4 and 7π/4, it gives r = 6(√2/2) = 3√2 ≈ 4.24, which is shown approximately as 4. Thus choice D represents points on the curve.

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