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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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