Question

HELPPPPPP

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

r = 2 - 2 sin θ
r = 3 - 2 sin θ
r = 2 + 2 sin θ
r = 1 - 3 sin θ

Answer 1

I got a?

Answer 2

@Directrix

Answer 3

Where is the graph: The graph of a limacon curve is given.
Please post it. Thanks.

Answer 4

@Directrix Sorry!!

Answer 5

I'll see if I get A.

Answer 6

i'm going with Option A @sarahc

Answer 7

Since a limacon follows the following forms:
\[r = a\pm b \cos(\theta) \quad \text{or} \quad r = a \pm b \sin(\theta) \]
We know it must be a function of sine since its largest radius is at \[ \theta = \frac{3\pi}{2} \]

Since sin(x) is minimized at that angle, this would return the smallest radius. So it must be
\[r = a - b \sin(\theta) \]

As for a and b, we can see from the graph that the radius does become 0 at one point (r=0). It is also never negative, because this creates the second inner loop in a limacon. Since the range of sin(x) is [-1,1], the only way for the radius to be greater than or equal to zero is if:
\[ a = b\]

This gives us A as the answer

Answer 8

it does not use sine. this is from the textbook

Answer 9

r = 3 - cos θ
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