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Koordinat suatu titik A

Koordinat suatu titik A. (r cos α o ,r sin α o ). ( x,y ). A. ●. x = r cos α o. r. y. y = r sin α o. α o. x. Aturan kosinus. C. a. b. α. A. c. B. a 2 =. b 2 +c 2 - 2bc.cos α. Jarak titik A ke titik B. Diketahui titik A (x 1 ,y 1 ) dan titik B(x 2 ,y 2 ).

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Koordinat suatu titik A

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  1. Koordinatsuatutitik A (r cosαo,r sin αo) (x,y) A ● x = r cosαo r y y = r sinαo αo x

  2. Aturankosinus C a b α A c B a2 = b2+c2 - 2bc.cosα

  3. Jaraktitik A ketitik B Diketahuititik A (x1,y1) dantitik B(x2,y2) (x2- x1)2 + (y2- y1)2 AB2 = (x2,y2) B ● y2- y1 A (x1,y1) y2 ● x2- x1 y1 x1 x2

  4. Apakahbenar Cos(A – B )= cos A – cos B ? Cos(60 – 30 )o= cos 60o – cos 30o Cos 30 o= ½ – ½ √3 ?? ½ √3 = ½ – ½ √3 Selanjutnyakitaakanmencarirumus Cos(A – B )=

  5. Perhatikan slide berikutnya

  6. Apakah: 2(4+6)=2.4+2.6 ?3(8+12)=3.8+3.12 ?Jadia(b+c)=ab+acBagaimanadengancos (15+30) =cos 15 +cos 30

  7. (r cos b, r sin b ) B ● r (r cos a, r sin a ) A ● r b-a b a O (rcos b – r cos a)2+(rsin b – rsin a)2 AB2 = AB2 = 2r2 – 2r2cos a.cos b - 2r2sin a sin b r2 + r2 – 2r2cos (b-a) AB2 = AB2 = 2r2– 2r2cos (b-a)

  8. 2r2 – 2r2cos a.cos b - 2r2sin a sin b = 2r2– 2r2cos (b-a) Keduaruasdibagi 2r2 1 – cos a.cos b - sin a sin b = 1 –cos (b-a) cos (b-a) = cos a.cos b + sin a sin b cos (b-a)= cos a.cos b + sin a sin b

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