Open in App
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Chapter 29: Chapter 29

Problem 926

Next question

Find the solution set of \(\sin ^{2} \theta+\sin \theta=0\).

Short Answer

Expert verified
The solution set of \(\sin ^{2} \theta+\sin \theta=0\) is given by \(\theta = 0 + n\pi\), where n is any integer or \(\theta = (-1)^{n}\pi\), where n is any odd integer.
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Try Premium for free

Over 22 million students worldwide already upgrade their learning with Vaia!

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Factor the given equation

When we analyze the given equation, we can factor out a common term like this: \[\sin\theta( \sin\theta + 1) = 0.\]

Step 2: Equate the factors to zero

Now, we have two factors that multiply to make zero. This means that at least one of the factors should be equal to zero. Thus, in solving this equation, we must consider both the possibilities: \[ \sin\theta = 0\] or \[ \sin\theta + 1 = 0. \]

Step 3: Solve for θ

Now, we solve each equation for \(\theta\): For the first equation: \(\sin\theta = 0\), we get \[\theta = 0 + n\pi, \] where n is any integer. For the second equation: \(\sin\theta + 1 = 0\), we get \[\sin\theta = -1,\] which has the general solution \[\theta = (-1)^{n}\pi, \] where n is any odd integer.

Step 4: Combine both sets of solutions

Finally, we can combine both families of solutions into a single set: \[\theta = 0 + n\pi, \] where n is any integer or \[\theta = (-1)^{n}\pi, \] where n is any odd integer. Now we've found the set of solutions that fulfill the given condition in the exercise. This set contains the general solutions for \(\theta\).

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 29

Find one number in the solution set of the equation \(\tan t=\sqrt{3}\).
Chapter 29

Prove the following two identities: (1) \(\cos (\pi / 2-\theta)=\sin \theta\) (2) \(\cos \theta=\sin (\pi / 2-\theta)\).
Chapter 29

Find the solution set of \(2 \cos ^{2} x-5 \cos x+2=0\).
Chapter 29

Solve: \(2 \cos 3 \mathrm{x}+1=0\)
Chapter 29

Find the solution set on \([0,2 \pi)\) for the equation $\cot ^{2} \theta+(1-\sqrt{3}) \cot \theta-\sqrt{3}=0$.
See all solutions

More chapters from the book ‘Algebra and Trigonometry’

See all chapters

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App
Create your free account now
Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Math

Pure Maths

Read Explanation
Math

Decision Maths

Read Explanation
Math

Mechanics Maths

Read Explanation
Math

Calculus

Read Explanation
Math

Geometry

Read Explanation
Math

Probability and Statistics

Read Explanation
View all explanations