trig

If cos A =1/3 with A in QIV find cscA/2

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  1. First find sin (A/2)= +/-sqrt[(1/2)(1 - cos A)]
    With A in the fourth quadrant, A/2 is in the second quadrant and sin A/2 is postive. Therefore
    sin (A/2) = -sqrt[(1/2)(2/3)]
    = sqrt(1/3)
    csc (A/2) is 1/cos(A/2)= sqrt 3

    check: A = 289.47 degrees
    A/2 = 144.736 degrees
    sin A/2 = 0.57735 = 1/(sqrt 3)
    csc A/2 = sqrt 3

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