1 Polar Coordinates GOALS: Using polar coordinates can simplify complicated rectangular equations. Students will convert from rectangular to polar and vice versa. The Language of Polar Graphs A polar coordinate system is a system to plot points in a plane with a point O in the center of a circular grid. The Pole is the point O, the origin. Polar Axis the horizontal ray from O pole (origin) to the right. Polar Coordinates of each point in the plane r = Directed distance from O to P. θ = Directed angle in a counter‐clockwise direction from polar axis to OP.
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1Polar Coordinates GOALS:
Usingpolarcoordinatescansimplifycomplicatedrectangularequations.Studentswillconvertfromrectangulartopolarandviceversa.
The Language of Polar Graphs
ApolarcoordinatesystemisasystemtoplotpointsinaplanewithapointOinthecenterofacirculargrid.
ThePoleisthepointO,theorigin.
PolarAxisthehorizontalrayfromOpole(origin)totheright.
PolarCoordinatesofeachpointintheplane
r=DirecteddistancefromOtoP.
=DirectedangleinacounterclockwisedirectionfrompolaraxistoOP.
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2Plotting Points in the Polar Coordinate System
EX#1:Plotthepointswiththegivenpolarcoordinates.
A. B.
A.
D.C.
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3Finding all Polar Coordinates of a Point
EX#2:Plotthepoint
Findthreeadditionalpolarrepresentationsofthispointon
or
B.Writetherestofthepossibilities:
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4Coordinate Conversion
Thepolarcoordinatesarerelatedtotherectangularcoordinatesasfollows:
EX#3:Findtherectangularcoordinatesofthepointswiththegivenpolarcoordinates.Useand
A.
B.
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5Converting Rectangular to Polar Coordinates
EX#4:Findtwopolarcoordinatepairsforthepointswithgivenrectangularcoordinates.
Use:and
Plotthepointsonbothcoordinategrids.
A.
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6B.
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7Equation Conversion from Polar Form to Rectangular Form
Ex#5A:Convertr=4torectangularformandidentifythegraph.Supportyouranswerwithapolargraphingutility.
Ex#5B:
Ex#5C:
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8Converting Equations from Rectangular to Polar Form
EX#6:Convert topolarform.
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9EX#7:FindingDistanceUsingPolarCoordinates
Radardetectstwoairplanesatthesamealtitude.Theirpolarcoordinatesareand
Howfarapartaretheairplanes?UsetheLawofCosines:
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10
EXITTICKET:
1.Whataretherectangularcoordinatesfor
2.Findthepolarcoordinatesforthepoint
3.Converttorectangularform.Identifythegraph.
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