Question

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. a circular graph with an inner loop on the left [-5, 5] by [-5, 5] r = 3 + 2 cos θ r = 2 + 3 cos θ r = 2 + 2 cos θ r = 4 + cos θ

Answer 1

I’m Confused is there a picture

Answer 2

Without using a graphing calculator, an equation that is correct for the graph is: B. r = 2 + 3cosθ.

In Mathematics and Geometry, a Limacon is a type of equation for a polar graph (curve) of degree 4 and shaped like a heart. Also, the general form of the equation of a Limacon include the following;

r = a + bsin(θ)

r = a - bsin(θ)

r = a + bcos(θ)

r = a - bcos(θ)

Generally speaking, the curve of a limacon would have an inner loop when the value of b is less than the value of a;

b < a.

By critically observing the graph (see attachment), we can logically deduce that the limacon curve has an inner loop. Therefore, it must be represented by this equation r = 2 + 3cosθ because the value of b is less than the value of a;

b = 2

a = 3

b < a

2 < 3 (True).

Missing information:

The question is incomplete and the missing graphs are shown in the attached picture.