Transcript Graphs of other trigonometric functions

Graphs of other
trigonometric functions
Section 4.6

Period: 


 n
Domain:
2
(n is an integer)
Range:    ,  

Vertical asymptote:


x
y = tan x
x

2
 n
Graph of five periods of y = tan x

Left asymptote is the solution of

Right asymptote is the solution of bx  c   2

The midpoint between the two
asymptotes is an x-intercept of the graph

The period is the distance between two
consecutive asymptotes
Sketching the graph of
y = a tan(bx – c)
bx  c   
2

Period:

Domain: x  n 
 (n is an integer)
 Range:    ,  


Vertical asymptotes:
y = cot x
x  n
Graph of six periods of y = cot x

Left asymptote is the solution of

Right asymptote is the solution of bx  c  

The midpoint between the two
asymptotes is an x-intercept of the graph

The period is the distance between two
consecutive asymptotes.
Sketching the graph of
y =a cot(bx – c)
bx  c  0

To sketch the graph of a secant or
cosecant function, you should first make a
sketch of its reciprocal function. Use that
as a guide for the graph of the secant or
cosecant function, including its
asymptotes.
Graphs of the secant and cosecant
functions
Graph of y = sec x using the graph
of y = cos x as a guide
Graph of y = csc x using the graph
of y = sin x as a guide