1 / 14

Intro to Polar Coordinates

Intro to Polar Coordinates. •. θ. r. Points on a Plane. Rectangular coordinate system Represent a point by two distances from the origin Horizontal dist, Vertical dist Also possible to represent different ways Consider using dist from origin, angle formed with positive x-axis. (x, y). •.

artaxiad-jacobs
Download Presentation

Intro to 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. Intro to Polar Coordinates

  2. • θ r Points on a Plane • Rectangular coordinate system • Represent a point by two distances from the origin • Horizontal dist, Vertical dist • Also possible to represent different ways • Consider using dist from origin, angle formed with positive x-axis (x, y) • (r, θ)

  3. Plot Given Polar Coordinates • Locate the following

  4. Find Polar Coordinates • What are the coordinates for the given points? • A • A = • B = • C = • D = • B • D • C

  5. Converting Polar to Rectangular • Given polar coordinates (r, θ) • Change to rectangular • By trigonometry • x = r cos θy = r sin θ • Try = ( ___, ___ ) • r y θ x

  6. Converting Rectangular to Polar • • Given a point (x, y) • Convert to (r, θ) • By Pythagorean theorem r2 = x2 + y2 • By trigonometry • Try this one … for (2, 1) • r = ______ • θ = ______ r y θ x

  7. Polar Equations • States a relationship between all the points (r, θ) that satisfy the equation • Example r = 4 sin θ • Resulting values Note: for (r, θ) It is θ (the 2nd element that is the independent variable θ in degrees

  8. Graphing Polar Equations • Set Mode on TI calculator • Mode, then Graph => Polar • Note difference of Y= screen

  9. Graphing Polar Equations • Also best to keepangles in radians • Enter function in Y= screen

  10. Graphing Polar Equations • Set Zoom to Standard, • then Square

  11. Try These! • For r = A cos Bθ • Try to determine what affect A and B have • r = 3 sin 2θ • r = 4 cos 3θ • r = 2 + 5 sin 4θ Experiment with Polar Function Spreadsheet

  12. Write Polar Equation in Rectangular Form • Given r = 2 sin θ • Write as rectangular equation • Use definitions • And identitiesGraph the given equation for clues

  13. Write Polar Equation in Rectangular Form • Given r = 2 sin θ • We know • Thus • And

  14. Write Rectangular Equation in Polar Form • Consider 2x – 3y = 6 • As before, usedefinitions

More Related