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PP Section 9.7

# PP Section 9.7 - Curves in Polar Coordinates An equation...

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Curves in Polar Coordinates

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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.
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

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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 ) , 2 ( 2 ) , 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
Example Graph the equation r = 1 + sin θ . We could construct a table of values as in the previous example, but we will show an alternative method.

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