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Matematika
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1 Jawaban
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1. Jawaban azrin123
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