Find the exact value of the trig function below.

cos a/2 if cosa = - 31/49 (assume cos a/2 is negative)

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  1. we know cos (2x) = 2cos^2 x - 1
    so cos a = 2cos^2 (a/2) - 1
    -31/49 + 1 = 2cos^2 (a/2)
    18/49 = 2cos^2 (a/2)
    9/49 = cos^2 (a/2)
    cos (a/2) = ± 3/7
    but we were to assume that cos (a/2) is negative, so

    cos (a/2) = -3/7

    Check with your calculator

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