Question

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph.
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[-5, 5] by [-5, 5]

r = 2 + 2 sin \(\theta\)
r = 3 + sin \(\theta\)
r = 1 + 3 cos \(\theta\)
r = 1 + 3 sin \(\theta\)

Answer 1

@perl

Answer 2

r = 1 + 3 sin θ is the answer

Answer 3

Can you explain why please?

Answer 4

@praneet_r ?

Answer 5

yeah, the sin makes it surround the y axis. In the standard form, \[r=a \pm b \sin \theta\], a/b becomes smaller as the loop becomes bigger

Answer 6

Oh, okay :) Thanks!

Answer 7

you can also plug in values , theta = 0, pi/4, pi/2, pi, 3pi/2, 2pi

Answer 8

@perl thats also a way to do it

Answer 9

@praneet_r a/b becomes smaller as the inner loop becomes bigger, is that correct? can you justify this

Answer 10

i shouldn't have said it like that. it makes more sense to say that when a/b is less than 1, then the limacon has an inner loop

Answer 11

@perl