Final answer:
The question asks for a sketch of the limacon described by the polar equation r=3+3 cosθ, which is a mathematical concept involving polar coordinates. One finds points by calculating r for different θ values and plotting the corresponding Cartesian coordinates.
Step-by-step explanation:
The student's question about sketching the graph of the polar equation r=3+3 cosθ pertains to the subject of Mathematics, specifically in the area involving polar coordinates and graphing. In polar coordinates, a point in the plane is determined by its distance r from the origin and angle θ relative to the positive x-axis. The given polar equation describes a limacon, which is a type of curve. To sketch the graph of this equation, one should calculate the value of r for various values of θ, ranging from 0 to 2π.
The Cartesian coordinates (x, y) can be derived from polar coordinates using the relationships x = r × cosθ and y = r × sinθ. By substituting a range of θ values into the polar equation and calculating the corresponding r values, one can then convert these to Cartesian coordinates and plot them to visualize the curve.