Final answer:
To graph the polar equation r = cos(θ / 3), set the domain of θ from 0 to 6π to capture the full period of the cosine function when graphed in polar coordinates. Use the conversion formulas x = r × cos(θ) and y = r × sin(θ) to understand the relation to cartesian coordinates.
Step-by-step explanation:
To graph the polar equation r = cos(θ / 3), you'll need to use a graphing device and select an appropriate domain for θ. The equation represents the relationship between the radial distance r and the angle θ in polar coordinates. Since cosine functions have a period of 2π, and the angle is divided by 3, we will need to adjust the domain accordingly to account for this stretching. Specifically, we need to make sure that θ ranges over a domain of 6π to capture the full period of the curve.
Begin by setting up the graphing device to plot in polar coordinates. Then, input the equation and set the domain for θ from 0 to 6π. The graph will reveal the complete curve of the equation r = cos(θ / 3) once θ has traversed this range. Remember, the x and y coordinates in a cartesian system can be derived from polar coordinates using the formulas x = r × cos(θ) and y = r × sin(θ), illustrating the connection between the two systems.