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Polar and Rectangular Coordinates

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Rectangular to Polar Coordinates (x, y) (r, ?) r = (x2 y2) ? = tan-1(y/x) ... Express in Rectangular Form. Example 1. r = -3. r2 = 9. x2 y2 = 9. Example 2. r = 10. ... – PowerPoint PPT presentation

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Title: Polar and Rectangular Coordinates


1
Polar and Rectangular Coordinates
  • Section 9-3

2
Polar to Rectangular Coordinates
  • (r, ?) ? (x, y)
  • x rcos?
  • y rsin?
  • Example (-3, p/3)
  • (-3/2, -3v3/2)
  • Example (10, - 40)
  • (7.7, -6. 4)

3
Rectangular to Polar Coordinates
  • (x, y) ? (r, ?)
  • r v(x2 y2)
  • ? tan-1(y/x)
  • Make sure you know what quadrant ? is in!
  • Example P(- 4, 8)
  • r v80 8.9
  • tan-1 (8/-4) -63.4
  • ? 116.6
  • (8.9, 116.6)

4
Equations Expressed in Polar Form
  • Example 1
  • x2 y2 100
  • r2 100
  • r 10

5
Example 2
  • x 3
  • rcos ? 3
  • r 3/cos ?

6
Example 3
  • y -10
  • rsin ? -10
  • r -10/sin ?

7
Example 4
  • 2x2 2y2 5y
  • 2(x2 y2) 5(rsin?)
  • 2r2 5rsin?
  • 2r 5sin?
  • r (5/2) sin?

8
Express in Rectangular Form
  • Example 1
  • r -3
  • r2 9
  • x2 y2 9

9
Example 2
  • r 10 . 5cos? 8sin?
  • r(5cos? 8sin?) 10
  • 5rcos? 8rsin? 10
  • 5x 8y 10

10
Homework
  • P.486 15-25odd, 26-36even
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