/*! 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 49 Use a graph to solve the equatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 49

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

Short Answer

Expert verified
The solutions to the equation \(\tan x = 1\) on the interval \(-2 \pi, 2 \pi\) are \(x = -3\pi/4, \pi/4, 5\pi/4, -7\pi/4\).

Step by step solution

01

Plot the function and the line

Draw the graph of \(y=\tan x\) on the interval \(-2 \pi, 2 \pi\). Also, plot the line \(y=1\). The tangent function has a period of \(\pi\) and it has vertical asymptotes at odd multiples of \(\pi/2\). Make sure to take the asymptotes into account when plotting the graph.
02

Identify Intersection

Identify and mark the points of intersection between \(y=\tan x\) and \(y=1\). This gives the x-values that satisfy \(\tan x = 1\). For \(\tan x = 1\), \(x = \pi/4 + n\pi\), \(n \in Z\). Only includes those within the interval \(-2 \pi, 2 \pi\).
03

Evaluate the solutions

Evaluate the points of intersection between \(y=\tan x\) and \(y = 1\). By substituting \(x\) into the original equation, it is shown that these are indeed the solutions.

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 privately owned yacht leaves a dock in Myrtle Beach, South Carolina, and heads toward Freeport in the Bahamas at a bearing of \(S 1.4^{\circ} \mathrm{E}\) The yacht averages a speed of 20 knots over the 428 -nautical-mile trip. (a) How long will it take the yacht to make the trip? (b) How far east and south is the yacht after 12 hours? (c) A plane leaves Myrtle Beach to fly to Freeport. What bearing should be taken?

A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 3.5 feet from its low point to its high point (see figure), and it returns to its high point every 10 seconds. Write an equation that describes the motion of the buoy where the high point corresponds to the time \(t=0\) (figure cannot copy)

Fill in the blank. If not possible, state the reason. $$\text { As } x \rightarrow-\infty, \text { the value of } \arctan x \rightarrow\text { _____ } .$$

Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Describe the behavior of the function as \(x\) increases without bound. $$f(x)=e^{-x} \cos x$$

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

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Logic and Functions

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.