Steps to Graph Secant Function,

(similar steps for cosecant function, )

Example 1. Sketch one period of :

Step i. Write the function using the reciprocal definition of sec:

Step ii. Factor out B, if necessary:

Step iii. Find amplitude:

Step iv. Find period (you may use the assumption that ):

Step v. Sketch the "five points" (red dots) of cosine function:

Step vi. Reflect, if necessary:

Step vii. Shift horizontally, if necessary (blue squares):

Step viii. Draw vertical asymptotes (through the points on the x-axis):

Step ix. Shift vertically, if necessary (pink diamonds – note that you need only shift the maximum and minimum points):

Step x. Draw the curve (start at maximum points and go up; start at minimum points and go down):

NOTE 1: you need only draw one period.

NOTE 2: the secant function above does not quite fit with the points – this is due to the simplifying assumption that .