Graph y = sec ( x )

Solution: As with tangent we will have to avoid x's for which cosine is zero (recall that sec x =1/ cos x)

Secant will not present at

               x = ........, - 5 ∏/2 , - 3 ∏/2 , - ∏/2 , ∏/2, 3 ∏/2 , 5 ∏/2 ,........

and the graph will have asymptotes at these points. Following is the graph of secant on the range  - 5 ∏/2

Notice as well that the graph is always greater than 1 & less than -1.  It should not be terribly surprising.  Remember that -1 ≤ cos ( x ) ≤ 1 .  Hence, one divided by something less than one will be greater than 1.   Also,  1 / ±1 = ±1 and hence we get the following ranges for secant.

sec (? x)  ≥ 1  and      sec (? x)  ≤ -1