Multiple Choice
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9. Polar Equations
Graphing Other Common Polar Equations
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Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.
A
Cardioid
B
Limacon
C
Rose
D
Lemniscate
Verified step by step guidance1
Start by recognizing the general form of polar equations. The equation given is r = 1 - \sin\theta.
Understand the characteristics of different polar curves: Cardioids have the form r = a ± b\sin\theta or r = a ± b\cos\theta where a = b.
Compare the given equation r = 1 - \sin\theta with the standard form of a cardioid. Notice that it matches the form r = a - b\sin\theta with a = b = 1.
Recall that a cardioid is a special type of limaçon where the coefficients a and b are equal, resulting in a heart-shaped curve.
Conclude that the given equation r = 1 - \sin\theta represents a cardioid, based on its form and the equality of coefficients.
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