## Description

### Table of content:

College Algebra & Trigonometry © 2017

Chapter R:Review of Prerequisites

SectionR.1Sets and the Real Number Line

SectionR.2Integer Exponents and Scientific Notation

SectionR.3Rational Exponents and Radicals

SectionR.4Polynomials and Multiplication of Radicals

Problem Recognition Exercises Simplifying Algebraic Expressions

SectionR.5Factoring

SectionR.6Rational Expressions and More Operations on Radicals

Algebra for Calculus

Chapter 1:Equations and Inequalities

Section1.1Linear Equations and Rational Equations

Section1.2Applications with Linear and Rational Equations

Section1.3Complex Numbers

Section1.4Quadratic Equations

Problem Recognition Exercises Simplifying Expressions Versus Solving Equations

Section 1.5Applications of Quadratic Equations

Section1.6More Equations and Applications

Section1.7Linear, Compound, and Absolute Value Inequalities

Problem Recognition Exercises Recognizing and Solving Equations and Inequalities

Equations for Calculus

Chapter 2:Functions and Relations

Section2.1The Rectangular Coordinate System and Graphing Utilities

Section2.2Circles

Section2.3Functions and Relations

Section2.4Linear Equations in Two Variables and Linear Functions

Section2.5Applications of Linear Equations and Modeling

Problem Recognition Exercises Comparing Graphs of Equations

Section2.6Transformations of Graphs

Section2.7Analyzing Graphs of Functions and Piecewise-Defined Functions

Section2.8Algebra of Functions and Function Composition

Chapter 3:Polynomial and Rational Functions

Section3.1Quadratic Functions and Applications

Section3.2Introduction to Polynomial Functions

Section3.3Division of Polynomials and the Remainder and Factor Theorems

Section3.4Zeros of Polynomials

Section3.5Rational Functions

Problem Recognition Exercises Polynomial and Rational Functions

Section3.6Polynomial and Rational Inequalities

Problem Recognition Exercises Solving Equations and Inequalities

Section3.7Variation

Chapter 4:Exponential and Logarithmic Functions

Section4.1Inverse Functions

Section4.2Exponential Functions

Section4.3Logarithmic Functions

Problem Recognition Exercises Analyzing Functions

Section4.4Properties of Logarithms

Section4.5Exponential and Logarithmic Equations

Section4.6Modeling with Exponential and Logarithmic Functions

Chapter 5:Trigonometric Functions

Section5.1Angles and Their Measure

Section5.2Right Triangle Trigonometry

Section5.3Trigonometric Functions of Any Angle

Section5.4Trigonometric Functions Defined on the Unit Circle

Section5.5Graphs of Sine and Cosine Functions

Section5.6Graphs of Other Trigonometric Functions

Problem Recognition Exercises Comparing Graphical Characteristics of Trigonometric Functions

Section5.7Inverse Trigonometric Functions

Chapter 6:Analytic Trigonometry

Section6.1Fundamental Trigonometric Identities

Section6.2Sum and Difference Formulas

Section6.3Double-Angle and Half-Angle Formulas

Section6.4Product-to-Sum and Sum-to-Product Formulas

Section6.5Trigonometric Equations

Chapter 7:Applications of Trigonometric Functions

Section7.1Applications of Right Triangles

Section7.2The Law of Sines

Section7.3The Law of Cosines

Problem Recognition Exercises Solving Triangles Using a Variety of Tools

Section7.4Harmonic Motion and Combinations of Trigonometric Functions

Chapter 8:Trigonometry Applied to Rectangular and Polar Coordinate Systems and Vectors

Section8.1Polar Coordinates

Section8.2Graphs of Polar Equations

Problem Recognition Exercises Comparing Equations in Polar and Rectangular Form

Section 8.3Complex Numbers in Polar Form

Section8.4Vectors

Section8.5Dot Product

Chapter 9:Systems of Equations and Inequalities

Section9.1Systems of Linear Equations in Two Variables and Applications

Section9.2Systems of Linear Equations in Three Variables and Applications

Section9.3Partial Fraction Decomposition

Section9.4Systems of Nonlinear Equations in Two Variables

Section9.5Inequalities and Systems of Inequalities in Two Variables

Problem Recognition Exercises Equations and Inequalities in Two Variables

Section9.6Linear Programming

Chapter 10:Matrices and Determinants and Applications

Section10.1Solving Systems of Linear Equations Using Matrices

Section10.2Inconsistent Systems and Dependent Equations

Section10.3Operations on Matrices

Section10.4Inverse Matrices and Matrix Equations

Section10.5Determinants and Cramer’s Rule

Problem Recognition Exercises Using Multiple Methods to Solve Systems of Linear Equations

Chapter 11:Analytic Geometry

Section11.1The Ellipse

Section11.2The Hyperbola

Section11.3The Parabola

Problem Recognition Exercises Comparing Equations of Conic Sections and General Equation

Section11.4Rotation of Axes

Section11.5Polar Equations of Conics

Section11.6Plane Curves and Parametric Equations

Chapter 12:Sequences, Series, Induction, and Probability

Section12.1Sequences and Series

Section12.2Arithmetic Sequences and Series

Section12.3Geometric Sequences and Series

Problem Recognition Exercises Comparing Arithmetic and Geometric Sequences and Series

Section12.4Mathematical Induction

Section12.5The Binomial Theorem

Section12.6Principles of Counting

Section12.7Introduction to Probability

Online:Section A-1Proof of the Binomial Theorem

A-2Definition of Conics From a Fixed Point and Fixed Line

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