Which of the following best describes the graph of the polar equation ?
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
9. Polar Equations
Graphing Other Common Polar Equations
Multiple Choice
Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.
r=4sin2θ
A
Cardioid
B
Limacon
C
Rose
D
Lemniscate
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Verified step by step guidance1
Recognize the general form of the given polar equation: \( r = 4 \sin 2\theta \). This equation is in the form \( r = a \sin(n\theta) \) or \( r = a \cos(n\theta) \).
Identify the value of \( n \) in the equation. Here, \( n = 2 \).
Recall that when \( n \) is an integer greater than 1, the equation \( r = a \sin(n\theta) \) or \( r = a \cos(n\theta) \) represents a rose curve.
Understand that the number of petals in a rose curve is determined by \( n \). If \( n \) is even, the rose will have \( 2n \) petals. If \( n \) is odd, it will have \( n \) petals.
Since \( n = 2 \) is even, the rose curve described by \( r = 4 \sin 2\theta \) will have \( 2 \times 2 = 4 \) petals, confirming it is a rose.
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