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11 December, 10:47

Find an exact value. cosine of negative seven pi divided by twelve

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  1. 11 December, 11:16
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    We want to find cos (-7π/12).

    Let x = - (7π) / 12.

    Then 2x = - (7π) / 6.

    Note that

    cos (2x) = 2cos²x - 1, or

    cos x = + / - √ ([1 + cos (2x) ]/2)

    Because - (7π) / 6 is in the 3rd quadrant, with a reference angle of π/6.

    cos (-7π/6) = - cos (π/6) = - √3/2 = - 0.866.

    Also, - (7π) / 12 is in the 2nd quadrant, therefore it's cosine is negative.

    Therefore, obtain

    cos (-7π/12) = - √[0.5 * (1 - 0.866) ] = - 0.2588.

    Answer: - 0.2588
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