Multiple Choice
Graph
15. Polar Equations
Graphing Other Common Polar Equations
Struggling with Precalculus?
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
First, recognize the general form of polar equations. A cardioid has the form r = a + a cos(θ) or r = a + a sin(θ). A limaçon has the form r = a + b cos(θ) or r = a + b sin(θ), where a ≠ b. A rose curve has the form r = a cos(nθ) or r = a sin(nθ). A lemniscate has the form r^2 = a^2 cos(2θ) or r^2 = a^2 sin(2θ).
Examine the given equation: r = 3 + 2 cos(θ). Compare it to the general forms of the polar equations mentioned above.
Notice that the equation r = 3 + 2 cos(θ) fits the form of a limaçon, which is r = a + b cos(θ) or r = a + b sin(θ), where a ≠ b.
In this equation, a = 3 and b = 2. Since a ≠ b, this confirms that the equation represents a limaçon.
Therefore, based on the comparison with the general forms, the given equation r = 3 + 2 cos(θ) is identified as a limaçon.
3:47mWatch next
Master Introduction to Common Polar Equations with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
Graphing Other Common Polar Equations practice set
Problem sets built by lead tutorsExpert video explanations