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If sinx=(-15)/17 with π≤x≤3π/2 and cosy=3/5 with 0≤y≤π/2, find the exact value of cos⁡(x-y)

User Thell
by
6.2k points

1 Answer

5 votes

Answer:

  • sin(x)=(-15)/17
  • cos(x)=(-8)/17
  • cos(y)=3/5
  • sin(y)=4/5


→\cos(x - y) = \cos(x)\cos(y) + \sin(x) \sin(y) \\ =(( - 8)/(17)* (3)/(5)) +(( - 15)/(17) * (4)/(5)) \\ = ( - 24)/(85) + ( - 60)/(85) \\ = ( (- 24) + ( - 60))/(85) \\ = \boxed{ ( - 84)/(85) }✓

(-84)/85 is the right answer.

User Pavlo Shandro
by
6.5k points
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