Inspect the four given graphs, which are plotted in polar coordinates (and shown in an attached .doc file), and choose the graph that corresponds to the polar equation r = 6 - (cos theta).© BrainMass Inc. brainmass.com March 4, 2021, 6:08 pm ad1c9bdddf
We will use characteristics of the given polar equation to identify the graph that corresponds to the given equation.
Since the value of the function cos theta ranges from -1 to +1, the value of r ranges from 6 - 1 (= 5) to 6 - (-1) (= 6 + 1 = 7), so every point of the graph of r = 6 - (cos theta) will be plotted at a distance of 5 to 7 units from the origin.
Using that fact, we can immediately eliminate graph A, since all the points of graph A are less than 5 units ...
Characteristics of three of the given graphs are used to eliminate them as candidates for the graph of the given equation, and a few key points of the remaining graph are checked and verified.