diberikan cos A = 12/13 dan A di kuadran I . sin B =15/17 dan B di kuadran II . hitunglah : a. cos ( A+B) b. sin ( A+B) c. sin ( A- B) d. cos ( A-B)
Matematika
dianauliaanwar
Pertanyaan
diberikan cos A = 12/13 dan A di kuadran I . sin B =15/17 dan B di kuadran II . hitunglah :
a. cos ( A+B)
b. sin ( A+B)
c. sin ( A- B)
d. cos ( A-B)
a. cos ( A+B)
b. sin ( A+B)
c. sin ( A- B)
d. cos ( A-B)
1 Jawaban
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1. Jawaban ariyat
cos A = 12/13
sin A = 5/13
sin B = 15/17
cos B = -8/17
a) cos (A+B) = cos A cos B - sin A sin B
= 12/13 × -8/17 - (5/13 × 15/17)
= -96/221 - 75/221
= -171/221
b) sin (A+B) = sin A cos B + cos A sin B
= 5/13 × -8/17 + (12/13 × 15/17)
= -40/221 + 180/221
= 140/221
c) cos (A-B) = cos A cos B + sin A sin B
= 12/13 × -8/17 + (5/13 × 15/17)
= -96/221 + 75/221
= -21/221
d) sin (A-B) = sin A cos B - cos A sin B
= 5/13 × -8/17 - (12/13 × 15/17)
= -40/221 - 180/221
= -220/221