Calculus

find the exact value of sin 11pi/12 using the sum or difference formula.

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  1. 11/12 = 2/12 + 9/12 = 1/6 + 3/4
    sin pi/6 = 1/2
    cos pi/6 = (1/2) sqrt 3
    sin 3 pi/4 = (1/2)sqrt 2
    cos 3 pi/4 = -(1/2) sqrt 2

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  2. Some students feel more comfortable working with degrees.
    sin(11π/12) = sin 165° = sin 15° by the CAST rule

    sin15° = sin(45°-30°)
    = sin45°cos30° - cos45°sin30°
    = (√2/2)(√3/2) - (√2/2)(1/2)
    = (√6 - √2)/4

    sin 11π/12 = (√6-√2)/4

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