Final answer:
To graph the polar function r(θ) = sin(2θ), substitute different values of θ into the function, calculate the values of r, and convert the polar coordinates to Cartesian coordinates to plot the graph.
Step-by-step explanation:
To graph the polar function r(θ) = sin(2θ), we can plot points by substituting different values of θ into the function. The angle θ can vary from 0 to 2π (or 0 to 360 degrees) to cover one complete revolution on the polar plane. For each value of θ, calculate the value of r using the given function, and then convert the polar coordinates (r, θ) to Cartesian coordinates (x, y). Plot these (x, y) points on a graph, and connect them to form the graph of the polar function.