The perfect way to define sine is through a right angled triangle. In the most basic form, sine is a ratio between the perpendicular and the hypotenuse. So basically, sin α = perpendicular/hypotenuse, with α being the angle between these two lines.
Sine can also be defined as a function of an angle, but the magnitude is always given in radians. In modern day mathematics, it is known as a solution to certain differential equations. The function, in real numbers, will range between negative infinity to positive infinity.
Image Courtesy: conservapedia.com
Arsine (or Sine inverse)
The inverse of sine is an arcsine. This function is used to calculate the angle between any two sides which are given in terms of real numbers. The domain and the co-domain in this case is the opposite of a sine function, and shaped backwards. It definitely relates to the sine function as the co-domain of a sine function is the domain of the arcsine function and vice versa. Mostly, the real numbers are mapped between the range of -1, +1 to R.
The single problem with this inverse function is in its validity. Mostly, the inverse function is not valid when the whole domain is selected from the original function. Basically, there is a violation in the definition of the function itself. This is the reason why the range of an inverse function of sine is restricted to -π, +π. This way, the different elements in a single domain do not get mixed with the elements included in the co-domain. Hence, when 1 is subtracted from sine, the range is from -1, +1 to -π, +π.
Image Courtesy: rapidtables.com