How do you know if $S(x)=sin x/ x$ is an even or odd function?

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Answer 1 · 2015-11-21T04:40:16

$S(x)$ is an even function.

A function is EVEN if $f(-x)=f(x)$ . A function is ODD if $f(-x)=-f(x)$ .

Let's find $S(-x)$ .

$S(-x)=stackrel"equal to -sin(x)"overbrace(sin(-x)/-x$

$S(-x)=(-sin(x))/-x$

$S(-x)=sin(x)/x=S(x)$

Thus, S(x) is an even function.

How do you know if S(x)=sin x/ xS(x)=sin x/ x is an even or odd function?