# Intermediate Algebra with Trigonometry

## 1st Edition

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eBook ISBN: 9781483218755
Published Date: 1st January 1983
Page Count: 716
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## Description

Intermediate Algebra with Trigonometry focuses on principles, operations, and approaches employed in intermediate algebra with trigonometry.

The publication first elaborates on basic properties and definitions, first-degree equations and inequalities, and exponents and polynomials. Discussions focus on polynomials, sums, and differences, multiplication of polynomials, greatest common factor and factoring by grouping, inequalities involving absolute value, equations with absolute value, and multiplication, division, and order of operation for real numbers. The manuscript then ponders on rational expressions, quadratic equations, and rational expressions and roots. Topics include equations quadratic in form, quadratic formula, completing the square, multiplication and division of complex numbers, equations with radicals, simplified form for radicals, multiplication and division of rational expressions, and addition and subtraction of rational expressions. The text takes a look at triangles, trigonometric identities and equations, introduction to trigonometry, and sequence and series, including arithmetic progressions, trigonometric functions, tables and calculators, sum and difference formulas, and the law of sines and cosines.

The publication is a valuable reference for students and researchers interested in intermediate algebra with trigonometry.

1 Basic Properties and Definitions

1.1 Basic Definitions

1.2 The Real Numbers, Opposites, Reciprocals, and Absolute Value

1.3 Graphing Simple and Compound Inequalities

1.4 Properties of Real Numbers

1.5 Addition and Subtraction of Real Numbers

1.6 Multiplication, Division, and Order of Operation for Real Numbers

Summary and Review

Test

2 First-Degree Equations and Inequalities

2.1 First-Degree Equations

2.2 First-Degree Inequalities

2.3 Equations with Absolute Value

2.4 Inequalities Involving Absolute Value

2.5 Formulas

2.6 Word Problems

Summary and Review

Test

3 Exponents and Polynomials

3.1 Properties of Exponents I

3.2 Properties of Exponents II

3.3 Polynomials, Sums, and Differences

3.4 Multiplication of Polynomials

3.5 The Greatest Common Factor and Factoring by Grouping

3.6 Factoring Trinomials

3.7 Special Factoring

Summary and Review

Test

4 Rational Expressions

4.1 Basic Properties and Reducing to Lowest Terms

4.2 Division of Polynomials

4.3 Multiplication and Division of Rational Expressions

4.4 Addition and Subtraction of Rational Expressions

4.5 Complex Fractions

4.6 Equations Involving Rational Expressions

4.7 Word Problems

Summary and Review

Test

5 Rational Exponents and Roots

5.1 Rational Exponents

5.4 Multiplication and Division of Radical Expressions

5.6 Addition and Subtraction of Complex Numbers

5.7 Multiplication and Division of Complex Numbers

Summary and Review

Test

6.1 Solving Quadratic Equations by Factoring

6.2 Completing the Square

6.5 Word Problems

6.6 More on Inequalities

Summary and Review

Test

7 Linear Equations and Inequalities

7.1 Graphing in Two Dimensions

7.2 The Slope of a Line

7.3 The Equation of a Straight Line

7.4 Linear Inequalities in Two Variables

7.5 Variation

Summary and Review

Test

8 Systems of Linear Equations

8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables

8.3 Introduction to Determinants

8.4 Cramer's Rule

8.5 Word Problems

Summary and Review

Test

9 The Conic Sections

9.1 Graphing Parabolas

9.2 The Circle

9.3 Ellipses and Hyperbolas

9.4 Second-Degree Inequalities

9.5 Nonlinear Systems

Summary and Review

Test

10 Relations and Functions

10.1 Relations and Functions

10.2 Function Notation

10.3 Algebra with Functions

10.4 Classification of Functions

10.5 The Inverse of a Function

Summary and Review

Test

11 Logarithms

11.1 Logarithms Are Exponents

11.2 Properties of Logarithms

11.3 Common Logarithms and Computations

11.4 Exponential Equations and Change of Base

11.5 Word Problems

Summary and Review

Test

12 Sequences and Series

12.1 Sequences

12.2 Series and Summation Notation

12.3 Arithmetic Progressions

12.4 Geometric Progressions

12.5 The Binomial Expansion

Summary and Review

Test

13 Introduction to Trigonometry

13.1 Degrees, Radians, and Special Triangles

13.2 Trigonometric Functions

13.3 Tables and Calculators

13.4 Graphing I: Amplitude and Period

13.5 Graphing II: Phase Shift

Summary and Review

Test

14 Trigonometric Identities and Equations

14.1 Proving Identities

14.2 Sum and Difference Formulas

14.3 Double-Angle and Half-Angle Formulas

14.4 Solving Trigonometric Equations

Summary and Review

Test

15 Triangles

15.1 Definition II: Right Triangle Trigonometry

15.2 The Law of Sines

15.3 The Ambiguous Case

15.4 The Law of Cosines

Summary and Review

Test

Appendix A: Synthetic Division

Appendix B: The Discriminant

Appendix C: Table of Powers, Roots, and Prime Factors

Appendix D: Table of Common Logarithms

Appendix E: Table of Trigonometric Functions

Answers to Odd-Numbered Exercises and Chapter Tests

Index

No. of pages:
716
Language:
English