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1 November, 19:34

Using the definition of an even function, show that y = - cos x is even

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  1. 1 November, 22:12
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    A function is even if, for each x in the domain of f, f ( - x) = f (x). The even functions have reflective symmetry through the y-axis.

    We have then:

    f (x) = - cos x

    f (-x) = - cos (-x)

    On the other hand:

    cos (-x) = cos x

    So:

    - cos (-x) = - cos x

    Therefore, it is fulfilled:

    f ( - x) = f (x)

    Example:

    cos (pi / 2) = 0

    cos (-pi / 2) = 0
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