Modeling with Conic Sections and Polar Equations — Test

Question 19 • Precalculus

Which graph represents points on the polar curve r is equal to 2 plus 5 sine theta ?

Answer

Image with description On a polar coordinate plane, points are at (0, 0), (2, 0), (negative 2, pi), (3, StartFraction 3 pi Over 2 EndFraction), (7, StartFraction 3 pi Over 2 EndFraction).

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

Image with description On a polar coordinate plane, points are at (0, 0), (2, 0), (negative 2, pi), (3, StartFraction pi Over 2 EndFraction), (7, StartFraction pi Over 2 EndFraction).

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

Explanation

For r = 2 + 5 sin θ, at θ = 0 we get r = 2, giving the point (2, 0). At θ = π/2, r = 7, and at θ = 3π/2, r = −3; a negative radius of −3 at 3π/2 is equivalent to (3, π/2). Choice D includes these points. Its point (−2, π) is also equivalent to (2, 0), so it represents a point on the curve.

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