Multiple Choice
Graph
15. Polar Equations
Graphing Other Common Polar Equations
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
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
Understand the types of polar equations: Cardioid, Limaçon, Rose, and Lemniscate. Each has distinct characteristics based on their equations.
Recognize that a Rose curve is typically represented by equations of the form \( r = a \sin(n\theta) \) or \( r = a \cos(n\theta) \), where \( n \) determines the number of petals.
Identify the given equation \( r = 4 \sin(2\theta) \). Notice the presence of \( 2\theta \), which indicates the number of petals in the Rose curve.
Determine the number of petals: If \( n \) is even, the Rose curve will have \( 2n \) petals. In this case, \( n = 2 \), so the curve will have \( 4 \) petals.
Conclude that the equation \( r = 4 \sin(2\theta) \) represents a Rose curve with 4 petals, based on the form and the value of \( n \).
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