Answer:
The graph is a convex limacon.
Step-by-step explanation:
Polar equation is defined as
[tex]r=b+a\sin \theta[/tex] and [tex]r=b+a\cos \theta[/tex]
Types of limacon:
1. If b < a, then graph is a limacon with and inner loop.
2. If a < b < 2a, then graph is a dimpled limacon.
3. If 2a ≤ b, then graph is a convex limacon.
The given equation is
[tex]r=4+2\sin \theta[/tex]
Here b=4 and a=2.
[tex]2a=2(2)=4=b[/tex]
[tex]2a=4[/tex]
[tex]2a=b[/tex] [tex][\because b=4][/tex]
Since 2a ≤ b, therefore the graph is a convex limacon.
