Graphing Tangent and Cotangent Transformations Graphs of Tan

Graphing Tangent and Cotangent Transformations

Graphs of Tan x and Cot x n n The graphs of tangent, and cotangent are related to the graphs of sine and cosine. In order to graph each of the new functions and their transformations, it helps to graph sin x or cos x on the same axes first.

Graph of y = tan x n n n Since tan x = sin x / cos x, begin by graphing cos x (as a guide) with dotted lines. Draw in vertical asymptotes where cos x = 0. Now graph the parent function of tan x. (tangent goes “up hill”).

Example: Tangent Graph y=tan x on the graph below:

Example: Tangent Answer:

Graph of y = cot x n n n Since cot x = cos x / sin x, begin by graphing sin x (as a guide) with dotted lines. Draw in vertical asymptotes where sin x = 0. Now graph the parent function of cot x. (cotangent goes “down hill”).

Example: Cotangent Graph y = cot x on graph below:

Example: Cotangent Answer:

Graphing Transformations n n n To graph transformations of these four trig functions, first graph the transformation with the sine or cosine “base” graph, using dotted lines. Then add the asymptotes anywhere sine or cosine is at a “mid” (on sinusoidal axis). Finally add the rest of the sec x, csc x, tan x, or cot x graph!

EXAMPLES Graph two cycles of the following:

EXAMPLES CONTINUED

EXAMPLES CONTINUED

ASSIGNMENT n Graphing Tangent and Cotangent Worksheet