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

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Answer 1 · 2016-05-11T03:51:20

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

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..

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