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

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Answer 1 · 2017-06-11T10:03:23

Range for $sin(arctanx)$ is $[-1,1]$ , and domain is $(-oo,oo)$ .

$arctanx$ is always from $-pi/2$ to $pi/2$ , but here $x$ can take any value from $(-oo.oo)$ , which is domain for $sin(arctanx)$ .

But $sin(arctanx)$ can take values only from $[-1,1]$

Hence range for $sin(arctanx)$ is $[-1,1]$ .

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