PP 11.3-11.4

# Transform the equation from polar coordinates to

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Transform the equation from polar coordinates to rectangular coordinates. r = - cos sin θ θ r = - cos sin θ θ r r r 2 = - cos sin θ θ x y x y 2 2 + = - x x y y 2 2 0 - + + =

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Transform the equation from rectangular coordinates to polar coordinates. x y 2 3 = x y 2 3 = ( 29 r r cos sin θ θ 2 3 = r r 2 2 3 0 cos sin θ θ - =
An equation whose variables are polar coordinates is called a polar equation . The graph of a polar equation consists of all points whose polar coordinates satisfy the equation. 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 Polar graph paper can be used to graph polar equations.

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Identify and graph the equation: r = 2 pole. the from 2 distance a at points All : 2 = r r 2 4 = x y 2 2 4 + = Circle with center at the pole and radius 2. 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 4 3 2 1 0
Identify and graph the equation: = 3 θ π = 3 tan tan π θ = 3 1 y x = 3 1 y x = 3 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 4 3 2 1 0 θ π = 3

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Identify and graph the equation: r sin θ = - 2 θ θ sin sin r y r y = = y = - 2 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 4 3 2 1 0
Graphing in Polar Coordinates Graph the polar equation Construct a table of values to find the polar points on the graph and plot the points . θ sin 2 = r ) 0 , 0 ( 0 ) , 1 ( 1 ) , 7 . 1 ( ), , 7 . 1 ( 7 . 1 ) , 4 . 1 ( ), , 4 . 1 ( 4 . 1 ) , 1 ( ), , 1 ( 1 ) 0 , 0 ( 0 0 2 2 3 2 3 3 4 3 4 4 6 5 6 6 = = = = = = = = = = r r r r r r π θ θ θ θ θ θ π π π π π π π π π π π

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Example Sketch the curve with polar equation r = 2 cos θ.
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• Fall '09
• L. OLDEWURTEL
• Polar Coordinates, Sin, Cos, Coordinate system, Polar coordinate system

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