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TRIGONOMETRI JUMLAH DAN SELISIH DUA SUDUT

TRIGONOMETRI JUMLAH DAN SELISIH DUA SUDUT. Oleh : MOHAMMAD KHUSAINI, S.Pd SMA NEGERI 1 KAHAYAN HILIR. SK & KD. Silabus. Ingat Kls X. Sumber. A. Jarak dua titik AB 2 = ( x 1 - x 2 ) 2 - ( y 1 - y 2 ) 2 AB 2 = ( cos a - cos b) 2 - (sin a - sin b) 2

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TRIGONOMETRI JUMLAH DAN SELISIH DUA SUDUT

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  1. TRIGONOMETRIJUMLAH DAN SELISIH DUA SUDUT Oleh : MOHAMMAD KHUSAINI, S.Pd SMA NEGERI 1 KAHAYAN HILIR SK & KD Silabus Ingat Kls X Sumber

  2. A Jarakduatitik AB2= (x1- x2)2-(y1- y2)2 AB2= (cos a - cos b)2-(sin a - sin b)2 =cos2 a – 2cos a cos b + cos2 b+ sin2a - 2sin a sinb + sin2 b = cos2 a+ sin2a+ cos2 b+ sin2 b- 2cos a cos b - 2sin a sinb AB2=1+1-2(cos a cos b+ sin a sinb) ………. (1) a-b B Rumus Trigonometri Penjumlahan Dua Sudut a b O Bila r = 1 Koordinat A (x1,y1) Karena sin a = x1/r Maka sin a = x1 Sehinggakoordinat A(cos a, sin a) B(cos b, sin b)

  3. AB2= (cos(a-b) - 1)2- (sin(a-b)- 0)2 = cos2 (a-b) – 2cos (a-b) + 1 + sin2(a-b) = cos2 (a-b) + sin2(a-b) + 1 + – 2cos (a-b) = 1+ 1 – 2cos (a-b) AB2 = 2 – 2cos (a-b) …………. (2) Dari persamaan (1) dan (2) Cos (a-b) = cos a cos b+ sin a sinb Dengancara yang samamaka cos(a + b) = cos a cos b - sin a sin b sin(a + b)  = sin a cos b + cos a sin b sin(a - b)  = sin a cos b - cos a sin b A a-b a B O b Koordinat A(cos(a-b), sin(a-b)) B(1,0)

  4. Sudut Rangkap Karenaa+a=2a Makacos 2a = cos (a+a) cos 2a = cos2a - sin2 a = 2 cos2a - 1 = 1 - 2 sin2a sin 2a  = 2 sin a cos a Ingat

  5. ContohSoal Hitunglah nilai eksak dari sin 15o Jawab : Sin 15o = sin (45o – 30o ) = sin 45o cos 30o – cos 45o sin 30o = - =

  6. Sayamenyadaritugasinijauhdarisempurnauntukitu saran danmasukandariparapenikmatsangatsayaharapkan Terimakasih

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