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Persamaan Trigonometri Anggota kelompok : M. Arsyad Setiawan Bima Aria…

- - - - Bentuk Umum
        Sin x = Sin α
        Penyelesaian
        (i) x = α + k.360°
        (ii) x = (180° - α) + k.360
      - Contoh Soal
        The solution set of Sin x = 1/2, 0 ≤ x ≤ 360° is
        Sin x = 1/2
        Sin x = Sin 30°
        (i) x = 30°+ k.360°
        (ii) x = (180° - 30°) + k.360° = 150° + .360°
        k=0
        (i) x = 30° + 0.360° = 30°
        (ii) x = 150° + 0.360 + 150°
        HP = {30,150}
    - - Bentuk Umum
        Cos x = Cos α
        Penyelesaian
        x = ± α + k.360°
      - Contoh Soal
        The solution set of 2 cos x = 1, 0 ≤ x ≤ 360° is
        2 cos x = 1
        cos x = 1/2
        cos x = 60°
        (i) x = 60 + k.360
        (i) x = -60 + k.360
        k=0
        (i) x = 60° + 0.360 = 60°
        (ii) x = -60° + 0.360 = -60°
        k=1
        (i) x = 60° + 1.360 = 420°
        (ii) x = -60° + 1.360° = 300°
        HP = {60 ,300 }
    - - Bentuk Umum
        Tan x = Tan α
        Penyelesaian
        x = α + k.180°
      - Contoh Soal
        The solution set of tan x = 1/3√3, 0 ≤ x ≤ 360°
        tan x = 1/3√3
        tan x = tan 30°
        x = 30° + k.180°
        k=0
        x = 30° + 0.180° = 30°
        k=1
        x = 30° + 1.180° = 210°
        HP = {30 ,210}
- - - - -cos x = sin 270' - x
      - -sin x = sin (-x)
      - -cos x = cos(180' - x )
      - -sin x = cos (90' + x)
      - sin x = (90' - x)
      - cos x = sin(90' +x)
      - -tan x = tan (-x)
      - -cot x = tan (90' + x)
      - cot x = (90' - x)
    - - The solution set of tan(2x-40')-cot50'=0 for0' <x<360' is
        
        tan(2x-40')-cot50'=0
        
        tan(2x-40')=cot50'
        
        tan(2x-40')=tan(90'-50')
        
        tan (2x-40')=tan 40'
        
        2x -40'=40'+k.180
        
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- - - - 240° and 300°
- - - - 2y²+3y-5=0
        
        diselesaikan meggunakan pemfaktoran
        
        (2y+5)(y-1)
        
        y = -5/2 v y =1
        
        Ambil nilai y yang dapat mudah di ubah menjadi bentuk cosinus
        Menggunakan y =1
        Cosx=1
        Cosx=0°
        
        Untuk mencari himpunan gunakan persamaan cosinus
        x1 = a +k.360 v x2 = -a +k.360
        
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- - - - Himpunan penyelesaian dari
        sin2x°-√3 cos2x°=√3
        Untuk 0°<x<270°
        
        k=√1²-(-√3)²
        k=√1+3
        k=√4
        k=2
        
        tan a = sin/cos
        tan a = 1/-√3
        tan a = -√3/3
        a=150°
        
        2cos(2x-150°)=√3
        cos(2x-150°)=√3/2
        cos(2x-150°)= cos30°
        
        diselesaikan menggunakan persamaan cosinus
        
        2x-150°=30°+k.360°
        
        x = 90°+k.180°
        
        1 more item...
        
        2x-150°=-30°+k.360
        
        x=60°+k.180
        
        1 more item...