Discovering the Graphs of Secant and Cosecant
Objective: Sketch a graph of the y = sec x and y = csc x.
Procedure for secant function:
 Using the angles laid out along the x-axis find the values of sec x on
your unit circle and plot those values along the y-axis
 Identify any vertical asymptotes
 Using the points and the asymptotes with a smooth curve sketch the
secant function


2




4
4
2
3
4

5
4
3
2
7
4
2
Procedure for cosecant function:
 Using the angles laid out along the x-axis find the values of csc x on
your unit circle and plot those values along the y-axis
 Identify any vertical asymptotes
 Using the points and the asymptotes with a smooth curve sketch the
cosecant function
Answer the following:
1) What function does the shape of the secant function resemble?
cosecant function resemble?
2) What is the period of the (A) secant function (B) cosecant function?
3) What is the amplitude of the (A) secant function (B) cosecant function?
4) Find the period of the following functions:
a. y  csc 7 x
4
b. y  4 sec x
3
7
x
c. f x   5 csc
4
5) Indicate how the graph changes for each of the following:
a. y  5 sec 6 x  4
5
b. y  3 csc x  3
6
Graphing Secant and Cosecant
Graphing ONE CYCLE – No Horizontal Shift
Ex 1: Graph y  3sec x  1
Ex 2: Graph y   csc x  4
Graphing ONE CYCLE with a Horizontal Shift
Ex 3: Graph y  3sec
4
5
1

 x   1
2



Ex 4: Graph y   csc 9  x    4
3
