To sketch the graph of a polar equation a good first step is to sketch the graph in the Cartesian coordinate system. This will give a way to visualize how r changes with θ. The information about how r changes with θ can then be used to sketch the graph of the equation in the polar coordinate system.
9.4 Relations between Cartesian, Cylindrical, and Spherical Coordinates. Consider a cartesian, a cylindrical, and a spherical coordinate system, related as shown in Figure 1. Figure 1: Standard relations between cartesian, cylindrical, and spherical coordinate systems. The origin is the same for all three.
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