Matematika

Pertanyaan

tolong dikerjain serta caranya
tolong dikerjain serta caranya

1 Jawaban

  • Trigonometri
    A lancip danB tumpul

    tan A = 12/5 = y/x
    x= 5, y =12 -->  r = 13 (pitagoras)
    sin A = y/r= 12/13
    cos A = x/r = 5/13

    sin B = 4/5 = y/r
    y = 4, r = 5, --> x = 3 (pitagoras)
    cos B = - x/r = - 3/5
    tanB = - y/x = -4/3

    a. sin (A+B) = sin A cos B + cos Asin B = (12/13)(-3/5) + (5/13)(4/5)
    = -36/65 + 20/65
    = - 16/25

    b. Cos (A+B)= cos A cos B - sin A sin B = (5/13)(-3/5) - (12/13)(4/5)
    = - 15/65 - 48/65
    = - 63/65

    c. tan (A-B) = (tan A - tan B)/ ( 1 + tan A. tan B)
    = (12/5 - (-4/3)) / ( 1 + 12/5 x - 4/3)
    = (12/5 + 4/3) / ( 1 - 48/15)  kalikan 15/15
    = (36 + 20) /(15 - 48)
    = 56/-33
    = - 56/33