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

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