Question

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

Answer 1

Domain and range `arcsin(sinx)` is `(-oo,oo)`.

Explanation:

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

`arcsinu=x=>arcsin(sinx)=x`

i.e. `arcsin(sinx)=x`

as domain and range `x` is `(-oo,oo)`,

domain and range `arcsin(sinx)` is `(-oo,oo)`.