Pre-Calculus-check answers

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Use a sum or difference identity to find the exact value of sin 255 degrees

Answer: sqrt6-sqrt2/4

Thanks

  • Pre-Calculus-check answers -

    You might notice that 225 = 180 + 75
    so sin 255 = sin(180+75)
    = sin 180cos 75 + cos180sin75
    = -sin75

    now 75 = 45 + 30
    so sin(75) = sin(45+30)
    = sin45cos30 + cos45sin30
    = (1/√2)(√3/2) + (1/√2)(1/2) or
    = (√2/2)(√3/2) + )√2/2)(1/2)
    = (√6 + √2)/4

    so sin 255 = -(√6 + √2)/4

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