Graphs of other trigonometric functions
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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