How do you determine if ${sin}^{2} (x)$ $sin^2(x)$ is an even or odd function?

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Answer 1 · 2017-01-11T10:27:18

${sin}^{2} (x)$ $sin^2(x)$ is an even function.

A function $f (x)$ $f(x)$ is even if $f (- x) = f (x)$ $f(-x)=f(x)$ and function is odd if $f (- x) = - x$ $f(-x)=-x$ .

As $f (x) = {sin}^{2} (x)$ $f(x)=sin^2(x)$

$f (- x) = {sin}^{2} (- x)$ $f(-x)=sin^2(-x)$

= ${(sin (- x))}^{2}$ $(sin(-x))^2$

= ${(- sin (x))}^{2}$ $(-sin(x))^2$

= ${sin}^{2} (x)$ $sin^2(x)$

Hence ${sin}^{2} (x)$ $sin^2(x)$ is an even function.

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