Matematika

Pertanyaan

1. 2 cos (3x-30°)=√3 , 0≤x≤360°
2. tan (1/2x)= tan [tex] \pi [/tex] /6 0≤x≤2[tex] \pi [/tex]

mohon bantuannya

1 Jawaban

  • 1.
    2 cos (3x - 30°) = akar 3 , 0<_x<_360°
    cos (3x - 30°) = 1/2 (akar 3)
    cos (3x - 30°) = cos 30°
    3x - 30° = 30°
    3x = 30° + 30°
    3x = 60°
    x = 60°/3
    x = 20°
    atau
    2 cos (3x - 30°) = akar 3
    cos (3x - 30°) = 1/2 (akar 3)
    cos (3x - 30°) = cos 330°
    3x - 30° = 330°
    3x = 330° + 30°
    3x = 360°
    x = 360°/3
    x = 120°
    jadi hp nya adalah {20°,120°}

    2.
    tan (1/2 x) = tan phi/6 , 0<_x<_2phi
    tan (1/2 x) = tan 180°/6
    tan (1/2 x) = tan 30°
    1/2 x = 30°
    x = 30° × 2
    x = 60°
    x = 1/3 phi
    atau
    tan (1/2 x) = tan 210°
    1/2 x = 210°
    x = 210° × 2
    x = 420°
    x =/= 7/3 phi
    jadi hp nya adalah {1/3 phi}

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