/*! 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 79 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 79

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

Short Answer

Expert verified
The graph of \(y = \cot 2x\) will exhibit four cycles between 0 and \(2\pi\) due to its period of \(\pi/2\). It will resemble the shape of a regular cotangent function, but cycles twice as frequently.

Step by step solution

01

Identifying the Period of the Function

The cotangent function \(y=\cot x\) has a period of \(\pi\). The presence of the coefficient '2' with the variable 鈥榵鈥� in the function \(y=\cot 2x\) effectively halves the period of the regular cotangent function. Therefore, the period of this function will be \pi/2. From the period, we can then determine the interval to graph.
02

Setting the Viewing Rectangle

The function should be viewed for a period of \(2\pi\) as per the instructions. This is equivalent to four periods of the given function \(y = \cot 2x\). Therefore, it would be suitable to set the x-axis in the viewing rectangle from 0 to \(2\pi\), as it will show the behaviour of the function for at least two periods. The y-axis value can be set from -2 to 2 for a clear view of the function.
03

Plotting the Function

Finally, using a graphing utility, the function \(y=\cot 2x\) should be plotted. If the x-axis is rightly segmented based on the period and the y-axis is correctly positioned, the graph should show the behaviour of the function for at least two periods.

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

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. $$30.42^{\circ}$$

Without drawing a graph, describe the behavior of the basic cosine curve.

Graph \(f, g,\) and \(h\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi .\) Obtain the graph of h by adding or subtracting the corresponding \(y\) -coordinates on the graphs of \(f\) and \(g\) $$f(x)=-2 \sin x, g(x)=\sin 2 x, h(x)=(f+g)(x)$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I convert degrees to radians, I multiply by \(1,\) choosing \(\frac{\pi}{180^{\circ}}\) for 1

Biorhythm cycles provide interesting applications of sinusoidal graphs. But do you believe in the validity of biorhythms? Write a few sentences explaining why or why not.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.