Graphs of other trigonometric functions Section 4.6

y = tan x Period: Domain: (n is an integer) Range: Vertical asymptote:

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

y = cot x Period: Domain: (n is an integer) Range: Vertical asymptotes:

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.

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