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Math Help - Complex Trig function problem

  1. #1
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    Complex Trig function problem

    Hi, ive been given the following problem:

    We know that, for all z in C, cos2(z)+sin2(z) = 1.

    This does not imply that |cos(z)| =< 1 and |sin(z)|=< 1.

    Show in fact that, for all y in R,

    |cos(iy)| > 1/2exp(|y|), |sin(iy)| >= 1/2(exp(|y|)-1)

    i've managed to show the first part with |cos(iy)|, but dont know how to proceed with the second part, |sin(iy)|, any help would be great!!
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  2. #2
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    Re: Complex Trig function problem

    Attached
    Attached Thumbnails Attached Thumbnails Complex Trig function problem-001.jpg  
    Thanks from paulluap1991
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