# Algebra & Trigonometry, 4th edition

• Kirk Trigsted

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## Overview

### Hallmark features of this title

• The updated Interactive eTextbook adapts to devices and is easier to navigate. It has 800+ new high-definition videos that are playable within the eTextbook, and incorporates hundreds of worked-out examples and interactive figures.
• The Guided Notebook has been updated to better engage the student and follows the new version of the eTextbook. (Editable version included)
• New auto-scored Geogebra Sketching Exercises allow students to sketch graphs like they would by hand.
• Corequisite resources are now built in, with expanded review content in Chapter R and diagnostic assessments of prerequisite skills that can be personalized for student needs.

ISBN-13: 9780138062798

Subject: Precalculus, College Algebra & Trigonometry

Category: Algebra & Trigonometry

### R. Review Chapter

• R.1 Real Numbers
• R.2 A Review of Fractions and the Order of Operations
• R.3 The Properties of Integer Exponents
• R.4 Radicals and Rational Exponents
• R.5 Polynomials
• R.7 Factoring Polynomials
• R.8 Rational Expressions
• R.9 The Addition and Multiplication Properties of Equality
• Chapter Summary

### 1. Equations, Inequalities, and Applications

• 1.1 Linear and Rational Equations
• 1.2 Applications of Linear Equations and Rational Equations
• 1.3 Complex Numbers
• 1.5 Applications of Quadratic Equations
• 1.6 Other Types of Equations
• 1.7 Linear Inequalities in One Variable
• 1.8 Absolute Value Equations and Inequalities
• 1.9 Polynomial and Rational Inequalities
• Chapter Summary

### 2. The Rectangular Coordinate System, Lines, and Circles

• 2.1 The Rectangular Coordinate System
• 2.2 Circles
• 2.3 Lines
• 2.4 Parallel and Perpendicular Lines
• Chapter Summary

### 3. Functions

• 3.1 Relations and Functions
• 3.2 Properties of a Function's Graph
• 3.3 Graphs of Basic Functions; Piecewise Functions
• 3.4 Transformations of Functions
• 3.5 The Algebra of Functions; Composite Functions
• 3.6 One-to-One Functions; Inverse Functions
• Chapter Summary

### 4. Polynomial and Rational Functions

• 4.2 Applications and Modeling of Quadratic Functions
• 4.3 The Graphs of Polynomial Functions
• 4.4 Synthetic Division; The Remainder and Factor Theorems
• 4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra
• 4.6 Rational Functions and Their Graphs
• 4.7 Variation
• Chapter Summary

### 5. Exponential and Logarithmic Functions and Equations

• 5.1 Exponential Functions
• 5.2 Logarithmic Functions
• 5.3 Properties of Logarithms
• 5.4 Exponential and Logarithmic Equations
• 5.5 Applications of Exponential and Logarithmic Functions
• Chapter Summary

### 6. An Introduction to Trigonometric Functions

• 6.1 An Introduction to Angles: Degree and Radian Measure
• 6.2 Applications of Radian Measure
• 6.3 Triangles
• 6.4 Right Triangle Trigonometry
• 6.5 Trigonometric Functions of General Angles
• 6.6 The Unit Circle
• Chapter Summary

### 7. The Graphs of Trigonometric Functions

• 7.1 The Graphs of Sine and Cosine
• 7.2 More on Graphs of Sine and Cosine; Phase Shift
• 7.3 The Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
• 7.4 Inverse Trigonometric Functions I
• 7.5 Inverse Trigonometric Functions II
• Chapter Summary

### 8. Trigonometric Identities, Formulas, and Equations

• 8.1 Trigonometric Identities
• 8.2 The Sum and Difference Formulas
• 8.3 The Double-Angle and Half-Angle Formulas
• 8.4 The Product-to-Sum and Sum-to-Product Formulas
• 8.5 Trigonometric Equations
• Chapter Summary

### 9. Applications of Trigonometry

• 9.1 Right Triangle Applications
• 9.2 The Law of Sines
• 9.3 The Law of Cosines
• 9.4 Area of Triangles
• Chapter Summary

### 10. Polar Equations, Complex Numbers, and Vectors

• 10.1 Polar Coordinates and Polar Equations
• 10.2 Graphing Polar Equations
• 10.3 Complex Numbers in Polar Form; DeMoivre’s Theorem
• 10.4 Vectors
• 10.5 The Dot Product
• Chapter Summary

### 11. Conic Sections and Parametric Equations

• Introduction to Conic Sections
• 11.1 The Parabola
• 11.2 The Ellipse
• 11.3 The Hyperbola
• 11.4 Conic Sections in Polar Form
• 11.5 Parametric Equations
• Chapter Summary

### 12. Systems of Equations and Inequalities

• 12.1 Solving Systems of Linear Equations in Two Variables
• 12.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method
• 12.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination
• 12.4 Partial Fraction Decomposition
• 12.5 Systems of Nonlinear Equations
• 12.6 Systems of Inequalities
• Chapter Summary

### 13. Matrices

• 13.1 Matrix Operations
• 13.2 Inverses of Matrices and Matrix Equations
• 13.3 Determinants and Cramer's Rule
• Chapter Summary

### 14. Sequences and Series; Counting and Probability

• 14.1 Introduction to Sequences and Series
• 14.2 Arithmetic Sequences and Series
• 14.3 Geometric Sequences and Series
• 14.4 The Binomial Theorem
• 14.5 Mathematical Induction
• 14.6 The Theory of Counting
• 14.7 An Introduction to Probability
• Chapter Summary

### Appendices

• A: Degree, Minute, A Second Form and Degree Decimal Form
• B: Conic Section Proofs
• B.1 Parabola Proofs
• B.2 Ellipse Proofs
• B.3 Hyperbola Proofs

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