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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. Initial ray A polar coordinate pair determines the location of a point.
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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. x-axis A polar coordinate pair
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is a polar function in which the length r is a function of the angle Some curves are easier to describe with polar coordinates: …but how to plot such a function…
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is a polar function in which the length r is a function of the angle Some curves are easier to describe with polar coordinates:
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is a polar function in which the length r is a function of the angle Some curves are easier to describe with polar coordinates: …but how can this be?
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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. x-axis
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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. x-axis But what about this coordinate pair?
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is a polar function in which the length r is a function of the angle Some curves are easier to describe with polar coordinates: …but how can this be?
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(Circle centered at the origin) Some curves are easier to describe with polar coordinates: (Try graphing it on your calculator) (Line through the origin whose slope is )
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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, ) is on the graph,so is (r, - ).
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Tests for Symmetry: y-axis: If (r, ) is on the graph,so is (r, - )or (-r, - ).
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Tests for Symmetry: origin: If ( r, ) is on the graph,so is (- r, )or ( r, + ).
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Tests for Symmetry: If a graph has two symmetries, then it has all three:
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Converting to Cartesian Coordinates Remember the unit circle?
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Converting to Cartesian Coordinates Convertto polar coordinates Graph this on your calculators for comparison
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