/*! 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 96 Determine whether the statement ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 96

Determine whether the statement is true or false. Justify your answer. The graph of \(y=\csc x\) can be obtained on a calculator by graphing the reciprocal of \(y=\sin x\).

Short Answer

Expert verified
The statement is false. While \(y=\csc x\) is indeed the reciprocal of \(y=\sin x\), simply graphing the reciprocal of \(y=\sin x\) on a calculator may not depict the true graph of \(y=\csc x\) with its vertical asymptotes and discontinuities.

Step by step solution

01

Understand the Functions

Take a few moments to recall the nature of the functions in question. The function \(y=\sin x\) is periodic and oscillates between -1 and 1. On the other hand, its reciprocal function \(y=\csc x\) is undefined at \(x= n\pi \), where \(n\) is an integer, because the sine function equals zero at these points.
02

Consider Calculator's Graphing Capabilities

Most standard calculators graph functions by plotting numerous points and then connecting these points with a line. Graphing the reciprocal of \(y=\sin x\) in a calculator may not correctly illustrate the vertical asymptotes and discontinuities present in the true graph of \(y=\csc x\), as the points where the function is undefined (i.e., where \(\sin x\) is zero) would be merely skipped over.
03

Finalize the Analysis

Based on this understanding, while the statement in question might technically seem correct at first glance, upon deeper inspection, it fails to accurately represent the complete nature of the function \(y=\csc x\) in terms of its discontinuities and vertical asymptotes, which are features that a standard calculator may struggle to handle effectively.

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

Sketch the graph of the function. Include two full periods. $$ y=\tan (x+\pi) $$

Sketch the graph of the function. Include two full periods. $$ y=\tan \frac{\pi x}{4} $$

Sketch the graph of the function. Include two full periods. $$ y=\csc (2 x-\pi) $$

Use the graph of the function to determine whether the function is even, odd, or neither. Verify your answer algebraically. $$ g(x)=\cot x $$

Sketch the graph of the function. Include two full periods. $$ y=3 \csc 4 x $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

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.