Matematika

Pertanyaan

tentukan hp :
a. cos x = -½ dengan 0 ≤ x ≤ 2π
b. Tan x = Tan 2π/5 dengan 0 ≤ x ≤ 2π
c. 1+ 2 cos 2x =0 dengan 0 ≤ x ≤ 360

1 Jawaban

  • a. cosx = -1/2
        cosx = cos120°
        x = 120° + k . 360°
        x = 120°
        x = -120° + k . 360°
        x = 240°
        HP = {120°, 240°}
        HP = {2/3π, 4/3π}

    b. tanx = tan2π/5
        tanx = tan72°
        x = 72° + k . 180°
        x = 72°, 252°
        HP = {72°, 252°}
        HP = {2/5π, 7/5π}

    c. 1 + 2cos2x = 0
        1 + 2(2cos²x - 1) = 0
        1 + 4cos²x - 2 = 0
        4cos²x - 1 = 0
        4cos²x = 1
        2cosx = 1
        cosx = 1/2
        cosx = cos60°
        x = 60° + k . 360°
        x = 60°
        x = -60° + k . 360°
        x = 300°
        HP = {60°, 300°}

    Semoga membantu

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