/*! 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 80 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 80

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\cot \frac{x}{2}$$

Short Answer

Expert verified
The graph of the function \(y = \cot (\frac{x}{2})\) shows the typical periodic behaviour of a cotangent function which repeats every \(2\pi\), due to the argument being \(\frac{x}{2}\).

Step by step solution

01

Understand the cotangent function

The cotangent function, \(\cot x\), is the reciprocal of the tangent function, \(\tan x\), (excluding \(x\) where \(\tan x = 0\)), with a period of \(\pi\) or 180 degrees. When the argument is \(\frac{x}{2}\), the period of the function doubles to \(2\pi\) or 360 degrees.
02

Determine the period of the function

The period of the function \(y = \cot x\) is \(\pi\). When the argument is \(\frac{x}{2}\), the period doubles to \(2\pi\). Therefore, the function \(y = \cot \frac{x}{2}\) has a period of \(2\pi\).
03

Use a Graphing Utility

Enter the function \(y = \cot (\frac{x}{2})\) into the graphing utility.
04

Set the viewing window

Adjust the viewing window so that it includes at least two periods of the function. The exact values will depend on the particular graphing utility, but with a period of \(2\pi\), it is recommended to set the x-range to cover at least from -\(4\pi\) to \(4\pi\) to show two full periods.
05

Graph the function

After setting the viewing window, graph the function. Notice the periodic nature of the graph, and be aware that there are undefined points (asymptotes) at each multiple of \(\pi\).

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

The toll to a bridge costs \(\$ 8.00 .\) Commuters who frequently use the bridge have the option of purchasing a monthly discount pass for \(\$ 36.00 .\) With the discount pass, the toll is reduced to \(\$ 5.00 .\) For how many bridge crossings per month will the cost without the discount pass be the same as the cost with pass? What will be the monthly cost for each option? (Section P.8, Example 3)

Use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds \(\left(D^{\circ} M^{\prime} S^{\prime \prime}\right)\) into decimal form, and vice versa. Convert each angle to \(D^{\circ} M^{\prime} S^{\prime \prime}\) form. Round your answer to the nearest second. $$50.42^{\circ}$$

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\tan \frac{x}{4}$$

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=-3 \cos \left(2 x-\frac{\pi}{2}\right)$$

This exercise is intended to provide some fun with biorhythms, regardless of whether you believe they have any validity. We will use each member's chart to determine biorhythmic compatibility. Before meeting, each group member should go online and obtain his or her biorhythm chart. The date of the group meeting is the date on which your chart should begin. Include 12 months in the plot. At the meeting, compare differences and similarities among the intellectual sinusoidal curves. Using these comparisons, each person should find the one other person with whom he or she would be most intellectually compatible.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Decision Maths

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.