What is a dimpled limacon?

Polar Curves

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Mathematics
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KG - University
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Hard
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1.
FLASHCARD QUESTION
Front
Back
A dimpled limacon is a type of polar curve that resembles a limacon with a dimple, characterized by its unique shape that has an inner loop and an outer loop.
2.
FLASHCARD QUESTION
Front
How many leaves does a rose curve with the equation r(θ) = a sin(nθ) have when n = 8?
Back
A rose curve with n = 8 has 8 leaves.
3.
FLASHCARD QUESTION
Front
What is the defining characteristic of a cardioid?
Back
A cardioid is a polar curve that resembles a heart shape and is defined by the equation r(θ) = a + b sin(θ) or r(θ) = a + b cos(θ) where a = b.
4.
FLASHCARD QUESTION
Front
How many leaves does a rose curve with the equation r(θ) = a sin(nθ) have when n = 9?
Back
A rose curve with n = 9 has 9 leaves.
5.
FLASHCARD QUESTION
Front
What is the general form of a rose curve?
Back
The general form of a rose curve is r(θ) = a sin(nθ) or r(θ) = a cos(nθ), where 'a' determines the length of the petals and 'n' determines the number of petals.
6.
FLASHCARD QUESTION
Front
What is the difference between a limacon and a dimpled limacon?
Back
A limacon can have different shapes, including a dimpled limacon, which specifically has a dimple or indentation in its inner loop, while a regular limacon may not have this feature.
7.
FLASHCARD QUESTION
Front
What is the equation of a cardioid in polar coordinates?
Back
The equation of a cardioid in polar coordinates can be expressed as r(θ) = a + a sin(θ) or r(θ) = a + a cos(θ).
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