How do I prove this statement? sin^-1(sin Ø) = Ø

Question

I can't figure out how to prove that statement. Any help would be great. 

Answer 1

Inverse sine of sine of x is x.

 

You chose an unfortunate symbol for your argument; it looks like the EMPTY SET symbol.

 

Far better choices would have been x, or any of these Greek lower case letters: α  β  θ  φ.

 

The 'proof' of this is based on the definition of an inverse function.