Question

How do you determine if `f(x)=1-cos x` is an even or odd function?

Answer 1

As #cos (-x)=cos x, f(-x)=f(x). So, f(x) is an even function.

Explanation:

If x is in radian unit, `cos x = sum(-1)^nx^(2n)/(n!), n=0, 1, 2...oo`.

As `(-x)^(2n)=x^(2n), cos(-x)=cos x, and f(-x)=f(x)`.

So, f(x) is an even function of x..