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    Graph of polar equation

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    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).

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    Solution Preview

    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 ...

    Solution Summary

    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.