Graphs of the Inverse Trig Functions
When we studied inverse functions in general (see Inverse Functions), we learned that the inverse of a function can be formed by reflecting the graph over the identity line y = x. We also learned that the inverse of a function may not necessarily be another function.
Look at the sine function (in red) at the right. If we reflect this function over the identity line, we will create the inverse graph (in blue). Unfortunately, this newly formed inverse graph is not a function. Notice how the green vertical line intersects the new inverse graph in more than one location, telling us it is not a function. (Vertical Line Test).
By limiting the range to see all of the y-values without repetition, we can define inverse functions of the trigonometric functions. It is possible to form inverse functions at many different locations along the graph. The functions shown here are what are referred to as the “principal” functions.