How to Graph Inverse of the Sine Function?

A step-by-step guide to graphing the inverse of the sine function

The inverse sine function (also called arcsine) is the inverse of the sine function. It is mathematically written as \(asin x\) (or) \(sin^{-1}x\) or \(arcsin x\). We read \(sin^{-1}x\) as “\(sin\) inverse of \(x\)”.

\(arcsin\:x=\:sin^{-1}x\:=\:inverse\:of\:sin\:x\)

If two functions \(f\) and \(f^{-1}\) are inverses of each other, then \(f(x) = y ⇒ x = f^{-1}(y)\). So \(sin x = y ⇒ x = sin^{-1}(y)\). That is when \(sin\) moves from one side to the other side of the equation, it becomes \(sin^{-1}\).

The graph of the inverse sine function with its range to the main branch \(\left[-\frac{\pi \:\:}{2},\:\frac{\pi \:}{2}\right]\) can be drawn using the table below.

Here, we have chosen random values for \(x\) in the domain of the inverse \(sin\) of \(x\), which is \([-1, 1]\). We know the values of the \(sin\) function and using the function of the inverse \(sin\) function, we have the following table.

By plotting these points on the graph, we get the inverse \(sin\) graph.