Matematika

Pertanyaan

mohon bantuannya yah
mohon bantuannya yah

1 Jawaban

  • untuk sudut istimewa (6, 8, 10)
    sin A = de/mi = 6/10     cos A = sa/mi = 8/10      tan A = de/sa = 6/8
    untuk sudut istimewa (9, 12, 15)
    cos B = sa/mi = 9/15     sin B = de/mi = 12/15    tan B = de/sa = 12/9

    a) sin 2A = sin (A + A) = sin A * cos A + cos A * sin A
                                        = (6/10)*(8/10) + (8/10)*(6/10) = 48/100 + 48/100                                            = 96/100 =
    24/25 atau 0,96

    b) cos 2B = cos (B + B) = cos B * cos B - sin B * sin B
                                          = (9/15)*(9/15) - (12/15)*(12/15) = 81/225 -144/225 =
    -63/225 atau -0,28

    c) sin (A-B) = sin (A + [-B]) = sin A*cosB - cos A*sin B
                                               = (6/10)*(9/15) - (8/10)*(12/15)=(54/150 - 96/150)  -42/150 atau -0,28

    d) cos (a + b) = cos A*cos B - sin A*sin B = (8/10)*(9/15) - (6/10)*(12/15)
                          = 72/150 - 72/150 = 0/150 = 0

    e) tan (a - b) = tan a - tan b / [ 1 + tan a * tan b ] =
        [6/8 + 12/9] / [1 + 6/8*12/9] = [6/8 + 12/9] / [1 + 72/72] = [6/8 + 12/9] / 2 =
                    (6*9 + 12*8 / 72) / 2 = (54+96 / 72) / 2 = (150/72)/ 2 =
    150/144 atau 1,0416667