Question

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

Answer 1

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]`.