Week_2_Lecture_1

# Week_2_Lecture_1 - MA211 Polar Coordinate System 1 Tests...

• Notes
• rajnath131313
• 28

This preview shows pages 1–9. Sign up to view the full content.

1 MA211 MA211 Polar Coordinate System

This preview has intentionally blurred sections. Sign up to view the full version.

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
3 Example . cos 2 3 sketch plot to - point and symmetry Use r Solution Test for Symmetry about the x -axis Replace by to get Thus 3 2cos is symmetric about the -axis. r x r cos 2 3 sin 0 cos 1 2 3 sin 0 sin cos 0 cos 2 3 0 cos 2 3 cos 2 3

This preview has intentionally blurred sections. Sign up to view the full version.

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

This preview has intentionally blurred sections. Sign up to view the full version.

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

This preview has intentionally blurred sections. Sign up to view the full version.

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
This is the end of the preview. Sign up to access the rest of the document.
• Fall '16
• Cos, Polar coordinate system, polar curves

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern