Week_2_Lecture_1 - MA211 Polar Coordinate System 1 Tests...

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1 MA211 MA211 Polar Coordinate System
2 Tests for Symmetry [1] About the x -axis [3] About the pole axis (or origin) We get back if we replace by . r f We get back if we replace by . r f We get back r = f ( ) if we replace by + . [2] About the y -axis
Example . cos 2 3 sketch plot to - point and symmetry Use r
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4 Test for Symmetry about the y -axis Thus 3 2cos is not symmetric about the -axis. r y get to by Replace r cos 2 3 sin 0 cos 1 2 3 sin sin cos cos 2 3 cos 2 3
5 Test for Symmetry about the origin Thus 3 2cos is not symmetric about the origin. r get to by Replace r cos 2 3 sin 0 cos 1 2 3 sin sin cos cos 2 3 cos 2 3
6 . 0 in for points plot those can we axis, - about the symmetric is 2cos 3 given that Thus, x r cos 2 3 r 0 5 3 2 3 2 4 3 2 1 Cardiod Then we reflect the points along the x -axis. (5,0) (4, /3) (3, /2) (2,2 /3) (1, )
7 Example 2 Sketch 4cos2 using symmetricity and point-plotting. r Symmetry The polar curve is symmetric about the x - and y -axes, and the origin. (Prove this.) Point-Plotting . together two the draw then and , and derive we example, for , 0 , plot that to Recall 2 x y x y x x y x y x y
8 CS. in the together two the draw then and , 2 cos 2 and 2 cos 2 derive we way, same In the polar r r

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