Inverse Secant  New
To investigate the graph of y = sec^{1}x, we need a graph of y = sec x. The easiest way to produce a graph of y = sec x is to start with a graph of y = cos x.  
From the graph of y = cos x it is easy to produce the graph of y = sec x = 1/cos x. The graph of y = sec x has a vertical asymptote where cos x = 0.


Now, select the largest possible domain of y = sec x that is onetoone. There is a slight difficulty here, since opinions differ as to which sections of the graph to pick. At right, the branches of the graph for the domain have been chosen (highlighed in blue). The range is . For another opinion, click here. 

You can obtain the graph of y = sec^{1}x (shown in red) by flipping the selected part of the graph of y = sec x (shown in blue) across the line y = x. The domain of sec^{1}x is and the range is . 

Inverse secant and its derivative ... 