L32 Polar Coordinates

L32 Polar Coordinates - 1 r = 3 2 r = 3 cos ± 5 ex...

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Lecture 32: Polar Coordinates The Cartesian Coordinates of a point ( x;y ) and its polar coordinates ( r;± ) are related by the equations x = r cos ± , y = r sin ± r 2 = x 2 + y 2 , tan ± = y x 1
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ex. Plot the points whose polar coordinates are (1 ; ± 4 ) ; (1 ; ± 2 ) ; ( ± 1 ; ± ± 2 ) ; (4 )( ± 4 ; 0) ; (2 ; ± ± 3 ) NOTE: In xy ± rectangular coordinates, every point P ( x;y ) has an unique representation,this is not true any more with Polar Coordinates. In fact, ( r;² ) = ( r;² ² 2 ) = ( ± r;² ² (2 n + 1) ± ) represent the same point. Negative r : By convention, negative sign means swing to the other side of the ray of angle ²: The pole is denoted by (0 ) for any angle ² . 2
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ex. Find 2 other pairs of polar coordinates of the point ( ± 1 ; ± ±= 2) ; one with r > 0, and one with r < 0. ex. Convert the point ( r;² ) = (3 ; 2 ± 3 ) from polar coordinates to Cartesian Coordinates. 3
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ex. Convert the point ( x;y ) = ( ± 1 ; ± p 3) from Cartesian Coordinates to polar coordinates. ex. Find a polar equation for the curve repre- sented by the given Cartesian equation. x 2 + y 2 = 4 4
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ex. Identify and Graph the polar curves by ±nding a Cartesian equation for the curve:
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Unformatted text preview: 1. r = 3 2. r = 3 cos ± 5 ex. Construct a polar equation for a circle of radius a with its center at x = a;y = 0. 6 ex. Graph the polar curve: r = cos 2 ± If you graph polar equations by plotting points, you will ±nd it helpful to know the symmetry in polar graphs. 7 Symmetry in Polar graphs: 1. If ( r;± ) is a point on the graph and ( r; ± ± ) is also a point on the graph, then the polar graph is symmetric with respect to the x ± axis (polar axis). 2. If ( r;± ) is a point on the graph and ( ± r;± ) is also a point on the graph, then the polar graph is symmetric with respect to the pole . 3. If ( r;± ) is a point on the graph and ( r;² ± ± ) is also a point on the graph, then the polar graph is symmetric with respect to the y ± axis (the vertical line ± = ²= 2). Tonight’s homework: sketch polar graphs. 8...
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This note was uploaded on 02/14/2012 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.

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L32 Polar Coordinates - 1 r = 3 2 r = 3 cos ± 5 ex...

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