How do you find the domain and range of $arcsin (sin x)$ $arcsin(sin x)$ ?

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Answer 1 · 2017-02-12T05:46:27

Domain and range $arcsin (sin x)$ $arcsin(sinx)$ is $(- \infty, \infty)$ $(-oo,oo)$ .

From the definition of $arcsin x$ $arcsinx$ , which is also described as ${sin}^{- 1} x$ $sin^(-1)x$ , if $sin x = u$ $sinx=u$ , we have

$arcsin u = x \Rightarrow arcsin (sin x) = x$ $arcsinu=x=>arcsin(sinx)=x$

i.e. $arcsin (sin x) = x$ $arcsin(sinx)=x$

as domain and range $x$ $x$ is $(- \infty, \infty)$ $(-oo,oo)$ ,

domain and range $arcsin (sin x)$ $arcsin(sinx)$ is $(- \infty, \infty)$ $(-oo,oo)$ .

How do you find the domain and range of arcsin(sinx) arcsin(sin x)?