Chapter 5 – Trigonometric Functions:
Unit Circle Approach
5.4 - More Trigonometric Graphs
Cosecant
Graphing
y = Acsc(Bx - C) +D

Graph the sine function with dotted lines.

The max point of the sine function is the
MINIMUM point of the cosecant function.

The min point of the sine function is the
MAXIMUM point of the cosecant function.

Where the sine function and y = D intersect are
the vertical asymptotes of the cosecant function.
Cosecant Example

Graph the following equation:
1


y  csc  x    1
4
4

Secant
Graphing
y = Asec(Bx - C) + D

Graph the cosine function with dotted lines.

The max point of the cosine function is the
MINIMUM point of the secant function.

The min point of the cosine function is the
MAXIMUM point of the secant function.

Where the cosine function and y = D intersect are
the vertical asymptotes of the secant function.
Secant Example

Graph the following equation:
3

y  3sec  x 
4


 1

Tangent
Graphing
y = Atan(Bx - C) + D

Find two consecutive asymptotes


2
 Bx  C 

2
A pair of consecutive asymptotes occur at
Bx  C  

2
and
Bx  C 

2

Find the point midway between the
asymptotes (this is the x-intercept if there
is no vertical shift; the y-value is the D).

Find the points on the graph that are ¼
and ¾ of the way between the
asymptotes. These points will have the
y-values of D+A and D-A respectively.
Tangent Example

Graph the following equation:


y  tan  x    2
4

Cotangent
Graphing
y = Acot(Bx - C) + D

Find two consecutive asymptotes
0  Bx  C  
A pair of consecutive asymptotes occur at
Bx  C  0 and
Bx  C  

Find the point midway between the
asymptotes (this is the x-intercept if there
is no vertical shift; the y-value is the D).

Find the points on the graph that are ¼
and ¾ of the way between the
asymptotes. These points will have the
y-values of –A+ D and A+D respectively.
Cotangent Example

Graph the following equation:
y  3cot  2x 
Graphing Summary
Graphing Summary