Question

What type of limacon is graphed by the polar equation r=4+2sinttheta?

Answer 1

The type of limacon graphed is a convex.

Answer 2

The graph is a convex limacon.

Explanation:

Polar equation is defined as

`r=b+a\sin \theta` and
`r=b+a\cos \theta`

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

`r=4+2\sin \theta`

Here b=4 and a=2.

`2a=2(2)=4=b`

`2a=4`

`2a=b`
`[\because b=4]`

Since 2a ≤ b, therefore the graph is a convex limacon.