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

1 Answer

Shwetank Mauria

Jun 11, 2017

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

Explanation:

#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]#.

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