PP 11.3-11.4

# PP 11.3-11.4 - Polar Coordinates P =(r r O Pole Polar axis...

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Polar Coordinates

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Polar axis θ r ( 29 P r = , O Pole
Polar axis O Pole π 6 4 = 6 , 4 P s. coordinate polar using 6 4, point Plot the

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Polar axis s. coordinate polar using 3 2 0, point Plot the π 3 2 = 3 2 , 0 P Example
θ r ( 29 P r r = < , , 0 ( 29 Plotting r r , , < 0

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Polar axis O s. coordinate polar using 4 5 2, - point Plot the π 4 5 - 4 5 , 2 Example
Polar axis O s. coordinate polar using 3 2 2,- - point Plot the π 3 2 - 2 - - = 3 2 , 2 P Example

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( 29 A point with polar coordinates also can be represented by any of the following: r , θ ( 29 ( 29 r k r k k , , π θπ + - + + 2 2 or any integer ( 29 The polar coordinates of the pole are where can be any angle. 0, ,
Conversion between Polar Coordinates and Rectangular Coordinates ) , ( y x P r θ x y sin cos r y r x = = x y y x r = + = tan 2 2

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Find the rectangular coordinates of the point with the following polar coordinates: ( 29 3 , 5 π x r y r = = cos sin θ 2 5 2 1 5 3 cos 5 cos = = = = r x 2 3 5 2 3 5 3 sin 5 sin = = = = r y ( 29 ( 29 The rectangular coordinates of the point 5, 3 are 5 2 5 3 2 , .
Find polar coordinates of a point whose rectangular coordinates are . θ r α 2 2 2 2 ) 3 ( ) 1 ( + - = + = y x r 2 4 3 1 = = + = 3 1 3 tan - = - = = x y π = - = 3 2 3 ( 29 ). 3 2 (2, is 3 , 1 point for the s coordinate polar of set A - ) 3 , 1 ( - = P ) 3 , 1 ( - = P

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Transform the equation from polar coordinates to rectangular coordinates.
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PP 11.3-11.4 - Polar Coordinates P =(r r O Pole Polar axis...

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