cos(sinx)

The domain of cos A is from negative infinity to positive infinity.So , A can take on any real value.

so domain of cos(sinx) is

( -infinity , infinity )

Hi,

The domain is "the set of values x can take so that f(x) is valid"

As you can easily see, the domain of cos(sinx), sin(sinx), sin(cosx), cos(cosx) is the whole set of real numbers.

Similarly for

sin(sin(sin(sin(sin(sin(sin(sin(sinx))))))))

and so on.........