The relation [math]y=sin\left(x\right)[/math] is classified as a function because each and every angle (input) has 1 and only 1 sine ratio (output.) Consequently, these outputs always range from -1 to 1 (inclusive.)

No, it is not. In order for a relation to be a function, each input can have only one output. Yet in order for the [b]inverse relation[/b] to be a function, [b]each output [/b](of the [b]original function[/b]) can only have 1 input that maps to it. Yet this clearly isn't the case for the function [math]y=sin\left(x\right)[/math] because the [b]output[/b] 1/2, for example, has more than one input (angle) (ex's: [math]\frac{\pi}{6}[/math] and [math]\frac{5\pi}{6}[/math]) that map to it. (In fact, there exist infinitely many angles whose sine ratio is 1/2.) Therefore, the [b]inverse relation[/b] is not a function.

[b]Hint:[/b] Find a piece of the[b] original function[/b] over which this function is [b]ALWAYS INCREASING!!! [/b](That way, no [b]output[/b] can have no more than 1 input that maps to it!)