Answered: Sketch the graphs of each of the…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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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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