Matematika

Pertanyaan

Tolong jawab beserta jalannya ya
Tolong jawab beserta jalannya ya

1 Jawaban

  • 1.) sin(90° - α) = ¾
    ➝ cos α = ¾
    Ilustrasi segitiga
    |\
    |. \
    |... \
    |......\
    | x.... \ 4
    | .........\
    | ...........\
    | .............\
    |______α\
    ........3

    Maka x = √(4² - 3²)
    = √(16 - 9)
    = √7
    = √7

    sin α = √7 / 4
    tan α = √7 / 3

    cosec (180° + α) + tan (270° - α)
    = -cosec α + cot α
    = 2/√7 + 3/√7
    = 5/√7
    = 5√7 / 7

    2.)
    a. cos (270° + α) + cos (270° - α) + tan (270° + α)
    = sin α - sin α - cot α
    = -cot α

    b. sin x + cos (3/2 π - x)
    = sin x + cos (270° - x)
    = sin x - sin x = 0

    c. sin 45° sin 15° / cos 135° cos 105°
    = ½(cos (45° - 15°) - cos (45° + 15°)) / ½(cos (135° - 105°) + cos (135° + 105°))
    = (cos 30° - cos 60°) / (cos 30° + cos 240°)
    = (½√3 - ½) / (½√3 - ½)
    = 1