Matematika

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) 

1 Jawaban

  • 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

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