Final answer:
The question deals with sketching a limaçon from the polar equation r=3-3cos(θ) by converting polar coordinates to Cartesian coordinates and then plotting these points on a graph.
Step-by-step explanation:
The student is asking to sketch the polar equation r=3-3cos(θ). To sketch this, we convert the polar coordinates to Cartesian coordinates using the relationship x = r x cos(θ) and y = r x sin(θ). As θ varies from 0 to 2π, we plot the points and obtain the graph of the equation. This particular equation is known for producing a limaçon, a type of polar graph with a characteristic 'loop' or 'dimple' depending on the coefficients involved.
To provide a step-by-step sketch:
- Start with θ = 0 and increment the angle in small steps.
- Calculate the corresponding r for each θ using the given polar equation.
- Convert these polar coordinates to Cartesian coordinates to plot on a standard xy-grid.
- Join the plotted points smoothly to reveal the shape of the graph.
This process will give a visual representation of the polar equation on a Cartesian plane.