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Persamaan Trigonometri, PERSAMAAN COSINUS, : (Zaky Ahmady S), : - Coggle…

- - - - The solution set of sin x = 1/2, 0° =< x =< 720° is..
        
        Sin x = 1/2
        Sin x = sin 30°
        (i)x =30°+ k.360°
        (i)x =(180-30)° + k.360°=150°+ k.360°
        K=0
        (i)x=30°+ 0.360°=30°
        (ii)x=150°+ 0.360°=150°
        K=1
        (i)x=30°+ 1.360°=390°
        (ii)x=150°+ 1.360°=510°
        K=2
        (i)x=30°+ 2.360°=30°+ 720°= 750° (TM)
        HP={30°, 150°, 390°, 510°}
    - - bentuk umum: sin x = sin a
- - - - penyelesaian
        
        √3 cos x + sin x = k cos (x-a)
        k = √3+1 = 2
        tan a = 1/√3 a=π/6
        2cos (x-π/6) = π/6) =√2
        (i)cos (x-π/6) = cos π/4 (x- π/6 ) = π/4 x= 5/12π
        (ii) cos (x-π/6) = cos (-π/4) (x-π/6) = -π/4 +2π x=-1/12π+2π=23/12π
- - - - Penyelesaian:
        tan x = ⅓ √3,0°≤ x ≤ 360°
        <=> 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°}
  - - - Contoh soal:
        The solution set of tan (2x - 40°) - cot50° = 0 for 0° < x < 360° is
        
        Penyelesaian:
        tan(2x - 40°) - cot 50° = 0
        <=> tan(2x - 40°) = cot 50°
        <=> tan(2x - 40°) = tan (90° - 50°)
        <=> tan(2x - 40°) = tan 40°
        => 2x - 40° = 40° + k.180°
        <=> 2x = 80° + k.180°
        <=> x = 40° + k.90°
        k = 0
        x = 40°
        k = 1
        x = 40° + 90° = 130°
        k = 2
        x = 40° + 180° = 220°
        k = 3
        x = 40° + 270° = 310°
        HP = {40°, 130°, 220°, 310°}
  - - - Contoh soal:
        The solution set of 2sin² x + 3sin x - 5 = 0 for 0° < x < 360° is
        
        Penyelesaian:
        2sin² x + 3sin x - 5 = 0
        Misal: sin x = a
        2a² + 3a - 5 = 0
        <=> (2a + 5) (a - 1) = 0
        <=> a = -5/2 a = 1
        => sin x = -5/2 sin x = 1
        karena nilai minimal dari fungsi sin x adalah -1 maka sin x = -5/2 tidak memenuhi, sehingga cukup memperhatikan sin x = 1
        sin x = 1
        <=> sin x = sin 90°
        (i)x = 90° + k.360°
        (ii)x = (180° - 90°) + k.360° = 90° + k.360°
        HP = {90°}