Graphs of other trigonometric functions

Section 4.6

y = tan x

Period:

Domain:(n is an integer)Range:

Vertical asymptote:

nx 2

nx 2

,

Graph of five periods of y = tan x

Sketching the graph of y = a tan(bx – c)

Left asymptote is the solution of

Right asymptote is the solution of

The midpoint between the two asymptotes is an x-intercept of the graph

The period is the distance between two consecutive asymptotes

2 cbx

2 cbx

y = cot x

Period:

Domain:(n is an integer)Range:

Vertical asymptotes:

nx

,

nx

Graph of six periods of y = cot x

Sketching the graph of y =a cot(bx – c)

Left asymptote is the solution of

Right asymptote is the solution of

The midpoint between the two asymptotes is an x-intercept of the graph

The period is the distance between two consecutive asymptotes.

0 cbx

cbx

Graphs of the secant and cosecant functions

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.

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