Matematika

Pertanyaan

Nilai sin 150 + sin 12
--------------------------- =
Cos 210 - cos 300

A. 2 D.1/2
B. 1 E. -1
C. 0

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2 Jawaban

  • (sin 150° + sin 120°)/(cos 210° - cos 300°)
    = (sin 30° + sin 60°)) / (- cos 30° - cos 60°)
    = (1/2 + 1/2 √3) / (-1/2 √3 - 1/2)
    = (1/2 + 1/2 √3) / -1(1/2 + 1/2 √3)
    = -1
  • sin 150 = sin ( 180 -30)
    = sin (30)
    sin 1/2
    sin 120 = sin 180 -60)
    sin = 1/2√3
    sin 1/2 + 1/2 √3= 1
    cos 270= cos (180+90)
    cos 90 =0
    cos 300 = -cos (360 - 60)
    cos 60 = -cos 1/2
    cos 270 +cos 300
    0 +-1/2
    = 1/2
    (1/2+1/2√3) 1/2= 2(1/2+1/2√3)= 1+√3

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