text: # math
  
  posted by .
  
  Use an Addition or Subtraction Formula to find the exact value of the expression.
  
  Sin(−5π/12)
  
  • math -
  
  some students have less difficulty if the angle is in degrees.
  Let's try this approach ....
  5π/12 radians = 75°
  
  so sin(-5π/12)
  = sin(-75°) which is in quadrant IV, making the sine negative
  = -sin(75°)
  = -sin(30° + 45°)
  = -(sin30cos45 + cos30sin45)
  = -( (1/2)(√2/2) + (√3/3)(√2/2) )
  = - √2/4 - √6/4
  
  so sin(05π/12) = -√2/4 - √6/4
  
  check:
  on my calculator:
  sin(-5π/12) = -.9659...
  and -√2/4 - √6/4 = -.9659..
  My answer is correct
  
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