/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 Use a graph to solve the equatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 52

Use a graph to solve the equation on the interval \(-2 \pi, 2 \pi\). $$\cot x=1$$

Short Answer

Expert verified
The solutions to the equation \( \cot x = 1 \) on the interval \( -2 \pi, 2 \pi \) are \( -\frac{3\pi}{4} , \frac{\pi}{4} ,\frac{5\pi}{4} \)

Step by step solution

01

Understanding the Cotangent function

Start by understanding that the cotangent function is the reciprocal of the tangent function. This means that the cotangent at any particular angle is the value of \( \frac{1}{\tan x} \) at that angle. It should also be noted that cotangent function has a period of \( \pi \) since the tangent function has a period of \( \pi \).
02

Plotting the Cotangent function

Plot a graph of cotangent function from \( -2 \pi \) to \( 2 \pi \). Where cotangent function is equals to 1, draw a horizontal line and identify these points on the x-axis.
03

Identifying the values

From the graph, the x-values where \( \cot x = 1 \) are \( -\frac{3\pi}{4} , \frac{\pi}{4} ,\frac{5\pi}{4} \) on the interval \( -2 \pi, 2 \pi \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A sprinkler on a golf green sprays water over a distance of 15 meters and rotates through an angle of \(140^{\circ} .\) Draw a diagram that shows the region that the sprinkler can irrigate. Find the area of the region.

Sketch a graph of the function. $$y=2 \arccos x$$

Data Analysis The table shows the average sales \(S\) (in millions of dollars) of an outerwear manufacturer for each month \(t,\) where \(t=1\) represents January. $$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Time, } t & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Sales, } S & 13.46 & 11.15 & 8.00 & 4.85 & 2.54 & 1.70 \\\ \hline \end{array}$$ $$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Time, } t & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \text { Sales, } S & 2.54 & 4.85 & 8.00 & 11.15 & 13.46 & 14.30 \\ \hline \end{array}$$ (a) Create a scatter plot of the data. (b) Find a trigonometric model that fits the data. Graph the model with your scatter plot. How well does the model fit the data? (c) What is the period of the model? Do you think it is reasonable given the context? Explain your reasoning. (d) Interpret the meaning of the model's amplitude in the context of the problem.

Determine whether the statement is true or false. Justify your answer. $$\tan \frac{5 \pi}{4}=1 \quad \rightarrow \quad \arctan 1=\frac{5 \pi}{4}$$

A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches. Its motion (in ideal conditions) is modeled by \(y=\frac{1}{4} \cos 16 t, t>0,\) where \(y\) is measured in feet and \(t\) is the time in seconds. (a) Graph the function. (b) What is the period of the oscillations? (c) Determine the first time the weight passes the point of equilibrium \((y=0)\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.