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Algebra and Trigonometry

Preface
1Prerequisites
2Equations and Inequalities
3Functions
4Linear Functions
5Polynomial and Rational Functions
6Exponential and Logarithmic Functions
7The Unit Circle: Sine and Cosine Functions
8Periodic Functions
9Trigonometric Identities and Equations
10Further Applications of Trigonometry
11Systems of Equations and Inequalities
12Analytic Geometry
13Sequences, Probability, and Counting Theory
AProofs, Identities, and Toolkit Functions
Answer Key
Index

Library Algebra and Trigonometry

Contents

Preface
1Prerequisites
2Equations and Inequalities
3Functions
4Linear Functions
5Polynomial and Rational Functions
6Exponential and Logarithmic Functions
7The Unit Circle: Sine and Cosine Functions
8Periodic Functions
9Trigonometric Identities and Equations
10Further Applications of Trigonometry
11Systems of Equations and Inequalities
12Analytic Geometry
13Sequences, Probability, and Counting Theory
AProofs, Identities, and Toolkit Functions
Answer Key
Index

Key Equations

Key Equations

Identity matrix for a $2 \times 2$ matrix	$I_{2} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] I_{2} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$
Identity matrix for a $3 \times 3$ matrix	$I_{3} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] I_{3} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$
Multiplicative inverse of a $2 \times 2$ matrix	$A^{−1} = \frac{1}{a d - b c} [\begin{matrix} d & - b \\ - c & a \end{matrix}], where a d - b c \neq 0 A^{−1} = \frac{1}{a d - b c} [\begin{matrix} d & - b \\ - c & a \end{matrix}],$

Key Equations · Algebra and Trigonometry · Physics Playground

2.6

2.6

Other Types of Equations

Other Types of Equations

2.7Linear Inequalities and Absolute Value Inequalities

2.7Linear Inequalities and Absolute Value Inequalities

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

3.6

3.6

Absolute Value Functions

Absolute Value Functions

3.7Inverse Functions

3.7Inverse Functions

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Exercises

Exercises

Review Exercises
Practice Test

Review Exercises
Practice Test

5.6

5.6

Rational Functions

Rational Functions

5.7Inverses and Radical Functions

5.7Inverses and Radical Functions

5.8Modeling Using Variation

5.8Modeling Using Variation

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

6.6

6.6

Exponential and Logarithmic Equations

Exponential and Logarithmic Equations

6.7Exponential and Logarithmic Models

6.7Exponential and Logarithmic Models

6.8Fitting Exponential Models to Data

6.8Fitting Exponential Models to Data

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Key Terms

Key Terms

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

10.6

10.6

Parametric Equations

Parametric Equations

10.7Parametric Equations: Graphs

10.7Parametric Equations: Graphs

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

11.6

11.6

Solving Systems with Gaussian Elimination

Solving Systems with Gaussian Elimination

11.7Solving Systems with Inverses

11.7Solving Systems with Inverses

11.8Solving Systems with Cramer's Rule

11.8Solving Systems with Cramer's Rule

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

13.6

13.6

Binomial Theorem

Binomial Theorem

13.7Probability

13.7Probability

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Chapter 9

Chapter 9

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Algebra and Trigonometry by OpenStax (Rice University), licensed under CC BY 4.0. Free to read at openstax.org. We changed the layout and left out notes meant only for teachers. OpenStax doesn't endorse this site.