Remarks

  1. We know from Chapter 1, that if \(y=f(x)\) is an invertible function, then \(x = f^{-1}(y)\). Thus, the graph of \(sin^{-1}\) function can be obtained from the graph of original function by interchanging x and y axes, i.e., if \((a, b)\) is a point on the graph of sine function, then \((b, a)\) becomes the corresponding point on the graph of inverse of sine function of sine function. Thus, the graph of the function \(y = sin^{-1}x\) can be obtained from the graph of \(y = sin x\) by interchanging x and y axes. The graphs of \(y = sin x\) and \(y = sin^{-1}x\) are as given in Fig 2.1 (i), (ii), (iii). The dark portion of the graph of \(y = sin^{-1}x\) represent the principal value branch.