1 / 17

Polar Coordinates

Polar Coordinates. MATH 1112 S. F. Ellermeyer. Rectangular vs. Polar Coordinates. Rectangular coordinates are the usual ( x,y ) coordinates.

renata
Télécharger la présentation

Polar Coordinates

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Polar Coordinates MATH 1112 S. F. Ellermeyer

  2. Rectangular vs. Polar Coordinates • Rectangular coordinates are the usual (x,y) coordinates. • Polar coordinates are (r,θ) coordinates – where θ is the directed angle measured in the usual way and r is the directed distance from the origin to the point in question. “Directed distance” means that we travel in the direction of the terminal side of θ if r>0 and in the opposite direction if r<0.

  3. The rectangular coordinates of a point are unique, but the polar coordinates are not unique. Every point has infinitely many polar coordinate representations.

  4. More Examples

  5. The Relationship between Rectangular and Polar Coordinates

  6. Polar vs. Rectangular Equations of Curves Some curves are easier to describe using equations in rectangular coordinates and some are easier to describe using polar coordinate equations. Curves that have a “circular” nature are the ones that are easier to describe using polar coordinates.

  7. r=8sin(θ)

  8. More Examples Graph r=1-sin(θ). Graph r=4sin(3θ). Graph r=4sin(5θ). Graph r=1-2sin(θ).

More Related