1 / 19

Polarkoordinater

Polarkoordinater. Kartesiske koordinater - Polarkoordinater. Kartesiske koordinater. Polarkoordinater. Koordinat-sammenheng. P. P. P. y. y. r. r. . . x. x. P = P(x,y). P = P(r,  ). x = r · cos  y = r · sin  r 2 = x 2 + y 2. Polarkoordinater Eks. P. r = 2.

kaiyo
Download Presentation

Polarkoordinater

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. Polarkoordinater

  2. Kartesiske koordinater - Polarkoordinater Kartesiske koordinater Polarkoordinater Koordinat-sammenheng P P P y y r r   x x P = P(x,y) P = P(r,) x = r·cos y = r·sin r2 = x2 + y2

  3. PolarkoordinaterEks P r = 2  =  / 6 Koordinatene r og  sies å være retningsbestemt. Eks: Med negativ verdi av r vil P befinne seg i motsatt retning av oppgitt vinkel.  / 6 2 P

  4. Polare ligninger og grafer x = r·cos y = r·sin r2 = x2 + y2 P y r  x 2 0 /4 a 3 2 1

  5. Polare grafer x = r·cos y = r·sin r2 = x2 + y2 P y r  x Kardeoide Rose Spiral Kjeglesnitt

  6. Fortrinn med polarkoordinater a 2 1

  7. Kjeglesnitt med polarkoordinater p rcos Q P = [r,] r x= - p O D e < 1 Ellips e = 1 Parabel e > 1 Hyperbel

  8. Kartesisk  Polar x = r·cos y = r·sin r2 = x2 + y2 P y r  x (x0,y0) · r (x0,y0) (0,2) · 2

  9. Polar  Kartesisk x = r·cos y = r·sin r2 = x2 + y2 P y r  x · (2,0) (2,0) (-4,0) (0,2) · 2 (0,-4)

  10. Kartesisk  Polar x = r·cos y = r·sin r2 = x2 + y2 P y r  x

  11. PolarkoordinaterSymmetri Symmetri om x-aksen: Symmetri om y-aksen: Symmetri om origo:

  12. PolarkoordinaterGraf Symmetri om x-aksen  = 2π/3 Ikke symmetri om y-aksen  = π  = 0 Ikke symmetri om origo  = 4π/3

  13. PolarkoordinaterAreal

  14. PolarkoordinaterAreal - Eks 1: Kardeoide

  15. PolarkoordinaterAreal - Eks 2  = 2π/3  = π  = 0  = 4π/3

  16. PolarkoordinaterAreal - Eks 3  = π/2  = -π/2

  17. PolarkoordinaterBuelengde

  18. PolarkoordinaterBuelengde - Eks 1

  19. END

More Related