Question

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

Answer 1

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