Matematika

Pertanyaan

tolong yaaa dari nomor 11 samapi 14 :)
terimah kasih:)
tolong yaaa dari nomor 11 samapi 14 :) terimah kasih:)

1 Jawaban

  • 11.
    sin A = 12/13
    180° <_ A <_ 270° (KUADRAN III)

    r = 13
    y = 12
    x^2 = r^2 - y^2
    = 13^2 - 12^2
    = 169 - 144
    = 25
    x = akar 25
    x = 5

    tan A = y/x
    = 12/5
    jadi nilai tan A adalah 12/5 (tan di kuadran III bernilai positif) (d)
    12.
    sin A = 3/5
    r = 5
    y = 3
    x^2 = r^2 - y^2
    = 5^2 - 3^2
    = 25 - 9
    = 16
    x = akar 16
    x = 4
    cotan A = x/y
    = 4/3
    jadi cotan A adalah 4/3 (e)
    13.
    sin 60° = 1/2 akar 3
    tan 60° = akar 3
    sin 45° = 1/2 akar 2
    cos 45° = 1/2 akar 2
    sin 60°.tan 60° + sin 45°.cos 45°
    = (1/2 akar 3)(akar 3) + (1/2 akar 2)(1/2 akar 2)
    = (1/2 × 3) + (1/4 × 2)
    = 3/2 + 2/4
    = 6/4 + 2/4
    = 8/4
    = 2
    (e) (soal salah => Nilai sin sin 60° ......harusnya
    Nilai sin 60° .......)
    14)
    sin 30° = 1/2
    cos 60° = 1/2
    sin 45° = 1/2 akar 2
    cos 30° = 1/2 akar 3

    sin 30° + cos 60°
    -------------------------- =
    sin 45° + cos 30°
    ..........1/2 + 1/2
    --------------------------------- =
    1/2 akar 2 + 1/2 akar 3
    ................1
    ---------------------------- =
    1/2(akar 2 + akar 3)
    ............2
    ---------------------- =
    akar 2 + akar 3
    ...........2 (akar 2 - akar 3)
    ----------------------------------------------- =
    (akar 2 + akar 3)(akar 2 - akar 3)

    2(akar 2 - akar 3)
    -------------------------- =
    ...........2 - 3

    2(akar 2 - akar 3)
    -------------------------- =
    ...............-1

    = -2(akar 2 - akar 3) (....)