Calculus 10'5

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10.5 Polar Coordinates
Greg Kelly, Hanford High School, Richland,
Washington
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One way to give someone directions is to tell
them to go three blocks East and five blocks
South.
Another way to give directions is to point and
say Go a half mile in that direction.
Polar graphing is like the second method of
giving directions. Each point is determined by a
distance and an angle.
A polar coordinate pair
Initial ray
determines the location of a point.
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Some curves are easier to describe with polar
coordinates
(Circle centered at the origin)
(Line through the origin)
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More than one coordinate pair can refer to the
same point.
All of the polar coordinates of this point are
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Tests for Symmetry
x-axis If (r, q) is on the graph,
so is (r, -q).
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Tests for Symmetry
y-axis If (r, q) is on the graph,
so is (r, p-q)
or (-r, -q).
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Tests for Symmetry
origin If (r, q) is on the graph,
so is (-r, q)
or (r, qp) .
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Tests for Symmetry
If a graph has two symmetries, then it has all
three
p