Answered: Sketch the graphs of each of the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 65E

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Question

Sketch the graphs of each of the following between x = -4p and x = 4p

y= cot x

Expert Solution

Step 1

We can graph $y = c o t x$ by observing the graph of the tangent function because these two functions are reciprocals of one another. Where the graph of the tangent function decreases, the graph of the cotangent function increases. Where the graph of the tangent function increases, the graph of the cotangent function decreases.

The cotangent graph has vertical asymptotes at each value of x where $\tan x = 0$ ; we show these in the graph below with dashed lines. Since the cotangent is the reciprocal of the tangent, $c o t x$ has vertical asymptotes at all values of x where $\tan x = 0$ , and $c o t x = 0$ at all values of x where $\tan x$ has its vertical asymptotes.

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