1 / 12

Polar Coordinates Polar and Rectangular Coordinates

Polar Coordinates Polar and Rectangular Coordinates. Packet 3. Polar vs. Rectangular Coordinates. For some real-world phenomena, it is useful to be able to convert between polar coordinates and rectangular coordinates. Polar vs. Rectangular Coordinates.

stedman
Télécharger la présentation

Polar Coordinates Polar and Rectangular 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 CoordinatesPolar and Rectangular Coordinates Packet 3

  2. Polar vs. Rectangular Coordinates For some real-world phenomena, it is useful to be able to convert between polar coordinates and rectangular coordinates.

  3. Polar vs. Rectangular Coordinates Suppose a rectangular coordinate system is superimposed on a polar coordinate system so that the origins coincide and the x-axis aligns with the polar axis, as shown at the right. Let P be any point in the plane. Polar Coordinates: P(r, θ) Rectangular Coordinates: P(x, y)

  4. Polar to Rectangular Coordinates Trigonometric functions can be used to convert polar coordinates to rectangular coordinates. The rectangular coordinates (x, y) of a point named by the polar coordinates (r, θ) can be found by using the following formulas: x = r cos θ y = r sin θ

  5. Rectangular to Polar Coordinates If a point is named by the rectangular coordinates (x, y), you can find the corresponding polar coordinates by using the Pythagorean Theorem and the Arctangent function (Arctangent is also known as the inverse tangent function).

  6. Rectangular to Polar Coordinates Since the Arctangent function only determines angles in quadrants 1 and 4 (because tangent has an inverse in quadrants 1 and 4) you must add π radians to the value of θ for points with coordinates (x, y) that are in quadrants 2 or 3.

  7. Rectangular to Polar Coordinates When x > 0, θ = When x < 0, θ =

  8. Rectangular to Polar Coordinates • When x is zero, . Why? • The polar coordinates (r, θ) of a point named by the rectangular coordinates (x, y) can be found by the following formulas: r = When x > 0 When x < 0

  9. Converting Equations • The conversion equations can also be used to convert equations from one coordinate system to the other. • Look at examples 4 and 5

  10. Examples Find the rectangular coordinates of each point. a. b. C(3, 270°)

  11. Example Find the polar coordinates of E(2, -4) Write the polar equation r = -3 in rectangular form.

  12. Example Write the rectangular equation x² + (y – 1)² = 1 in polar form.

More Related