Answer:
c. graph
Explanation:
The answer is c.
Let's learn detailly.
The graph of r=2cosθ is a limacon. A limacon is a type of curve that is similar to a circle, but it has two loops. The graph of r=2cosθ is created by plotting points that satisfy the equation r=2cosθ.
To graph r=2cosθ, you can use the following steps:
- 1. Choose a range of values for θ.
- 2. For each value of θ, calculate the corresponding value of r.
- 3. Plot the points (r,θ) on a polar coordinate system.
The following table shows some values of θ and the corresponding values of r: Attachment
Plotting these points on a polar coordinate system, you will get the following graph: Attachment
As you can see, the graph of r=2cosθ has two loops. The first loop is created when θ goes from 0 to π, and the second loop is created when θ goes from π to 2π. The graph is symmetric about the x-axis.
The limacon r=2cosθ is also called a cardioid. The name "cardioid" comes from the Greek word for "heart", because the graph resembles a heart shape.