Let's consider the equations of a limacon.
Equations of a Limacon [0.5 em]
r= a± bcosθ or r= a± bsinθ
It is noticeable that r=2+cos θ is a limacon equation. Limacons can be classified depending on the a and b values of the equation.
Limacon with Inner Loop
Cardioid
Dimpled Limacon
Convex Limacon
a/b<1
a/b=1
1< a/b< 2
a/b≥ 2
Let's identify the values of a and b in the given equation.
Equation of a Limacon [0.5 em]
r=2+cos θ ⇕ r= 2+ 1cos θ
We can see that a=2 and b=1. Therefore, the following inequality is true.
Convex Limacon Condition [0.5 em]
a/b≥ 2 ⇔ 2/1≥ 2 ✓
We found that the given equation represents a convex limacon. Let's take a look at its graph.
The graph confirms our answer. Finally, we can complete the given statement.
The equation r=2+cos θ represents a convex limacon.
