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Numbers 1 and 2 in Example 11.5.2 are examples of ‘lima¸ons,’ number 3 is an example of a ‘polar rose,’ and
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number 4 is the famous ‘Lemniscate of Bernoulli.’ 11.5 Graphs of Polar Equations 809 coordinate system, but also prepare you for what is needed in Calculus. Second, the symmetry
seen in the examples is also a common occurrence when graphing polar equations. In addition to
the usual kinds of symmetry discussed up to this point in the text (symmetry about each axis and
the origin), it is possible to talk about rotational symmetry. We leave the discussion of symmetry
to the Exercises. In our next example, we are given the task of ﬁnding the intersection points of
polar curves. According to the Fundamental Graphing Principle for Polar Equations on page 796,
in order for a point P to be on the graph of a polar equation, it must have a representation P (r, θ)
which satisﬁes the equation. What complicates matters in polar coordinates is that any given point
has in...

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