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