4.7.1 The graph of the secant function

The graph of secant function in £ £ p , x ≠ π , is shown in Fig. . . In the first and fourth quadrants or in the interval − < < , y = sec takes only positive values, whereas it takes only negative values in the second and third quadrants or in the interval π < < For £ £ p , x ¹ p , the secant function is continuous.

The value of secant function raises from to ¥ for x ∈  , π ; it raises from −∞ to - for x ∈  π π , . It falls from - to −∞ for x ∈  , and falls from ¥ to for x ∈  As y = sec is periodic with period p , the same segment of the graph for π , x ≠ π , is repeated in \ ]   \ Now, the entire graph of y = sec is shown in Fig. . .

. . Inverse secant function The secant function,sec : \ \ ]     is bijective in the restricted domain \ ]    . So, the inverse secant function is defined with  \ as its domain and with \ ]    as its range.

Definition . The inverse secant function sec : \ \ ]     is defined by sec ( ) x whenever sec y ]    \ Fig. . Fig.