/*! 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 918 Find the solution set for \(\sin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 29: Problem 918

Find the solution set for \(\sin \mathrm{x}=0\).

Short Answer

Expert verified
The solution set for \(\sin \mathrm{x} = 0\) is given by: \(x = 2n\pi\) or \(x = (2m + 1)\pi\), where n and m are integers.

Step by step solution

01

Identify the sine function's behavior

The sine function is a periodic function, which means it repeats its values in regular intervals. The sine function has a period of \(2\pi\), so every \(2\pi\), the sine function returns to its starting value. Therefore, we can expect multiple solutions that satisfy the equation \(\sin \mathrm{x} = 0\).
02

Determine when the sine function is equal to zero

The sine function is equal to zero at two points within one period: at the beginning and at the midpoint. Within the interval \(0 \leq x \leq 2\pi\), the sine function equals zero when \(x = 0\) and when \(x = \pi\). Since the sine function repeats its values every \(2\pi\), we can find all the other zero-valued points by adding integer multiples of \(2\pi\) to these two points.
03

Write the general solution for x

To find all the values of x for which \(\sin \mathrm{x} = 0\), we add integer multiples of \(2\pi\) to both \(0\) and \(\pi\): 1) \(x = 0 + 2n\pi\) where n is an integer, which can be written as \(x = 2n\pi\) 2) \(x = \pi + 2m\pi\) where m is an integer, which can be written as \(x = (2m + 1)\pi\) Combining these two solutions, we can find the complete solution set for the equation \(\sin \mathrm{x} = 0\):
04

Final Answer

The solution set for \(\sin \mathrm{x} = 0\) is given by: \(x = 2n\pi\) or \(x = (2m + 1)\pi\), where n and m are integers.

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

Prove the identity \(\left(\sin ^{2} \theta+\cos ^{2} \theta\right) / \cos ^{2} \theta=\sec ^{2} \theta\).

Prove that \(\cos ^{4} \mathrm{~B}-\sin ^{4} \mathrm{~B}=\cos ^{4} \mathrm{~B}-\sin ^{4} \mathrm{~B}\) is an identity.

Prove the following two identities: (1) \(\cos (\pi / 2-\theta)=\sin \theta\) (2) \(\cos \theta=\sin (\pi / 2-\theta)\).

Solve for \(\theta: \sin \theta+2 \tan \theta=0,0 \leq \theta \leq 2 \pi\).

Show that \(\tan (-v)=-\tan v\) for every number \(\mathrm{v}\) in the domain of the tangent function.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.