Algebra and Trigonometry

College Algebra and Trigonometry will appeal to those who want to give important topics more in–depth, higher–level coverage. This text offers streamlined approach accompanied with accessible definitions across all chapters to allow for an easy–to–understand read. College Algebra contains prose that is precise, accurate, and easy to read, with straightforward definitions of even the topics that are typically most difficult for readers.

Spis treści:
About the Author
Preface to the Instructor
Acknowledgments
Preface to the Student
1 The Real Numbers
1.1 The Real Line
Construction of the Real Line
Is Every Real Number Rational?
Problems
1.2 Algebra of the Real Numbers
Commutativity and Associativity
The Order of Algebraic Operations
The Distributive Property
Additive Inverses and Subtraction
Multiplicative Inverses and the Algebra of Fractions
Symbolic Calculators
Exercises, Problems, and Worked–out Solutions
1.3 Inequalities
Positive and Negative Numbers
Lesser and Greater
Intervals
Absolute Value
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions
2 Combining Algebra and Geometry
2.1 The Coordinate Plane
Coordinates
Graphs of Equations
Distance Between Two Points
Length, Perimeter, and Circumference
Exercises, Problems, and Worked–out Solutions
2.2 Lines
Slope
The Equation of a Line
Parallel Lines
Perpendicular Lines
Midpoints
Exercises, Problems, and Worked–out Solutions
2.3 Quadratic Expressions and Conic Sections
Completing the Square
The Quadratic Formula
Circles
Ellipses
Parabolas
Hyperbolas
Exercises, Problems, and Worked–out Solutions
2.4 Area
Squares, Rectangles, and Parallelograms
Triangles and Trapezoids
Stretching
Circles and Ellipses
Exercises, Problems, and Worked– ;out Solutions
Chapter Summary and Chapter Review Questions
3 Functions and Their Graphs
3.1 Functions
Definition and Examples
The Graph of a Function
The Domain of a Function
The Range of a Function
Functions via Tables
Exercises, Problems, and Worked–out Solutions
3.2 Function Transformations and Graphs
Vertical Transformations: Shifting, Stretching, and Flipping
Horizontal Transformations: Shifting, Stretching, Flipping
Combinations of Vertical Function Transformations
Even Functions
Odd Functions
Exercises, Problems, and Worked–out Solutions
3.3 Composition of Functions
Combining Two Functions
Definition of Composition
Order Matters in Composition
Decomposing Functions
Composing More than Two Functions
Function Transformations as Compositions
Exercises, Problems, and Worked–out Solutions
3.4 Inverse Functions
The Inverse Problem
One–to–one Functions
The Definition of an Inverse Function
The Domain and Range of an Inverse Function
The Composition of a Function and Its Inverse
Comments about Notation
Exercises, Problems, and Worked–out Solutions
3.5 A Graphical Approach to Inverse Functions
The Graph of an Inverse Function
Graphical Interpretation of One–to–One
Increasing and Decreasing Functions
Inverse Functions via Tables
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions
4 Polynomial and Rational Functions
4.1 Integer Exponents
Positive Integer Exponents
Properties of Exponents
Defining x0
Negative Integer Exponents
Manipulations with Exponents
Exercises, Problems, and Worked–out Solutions
4.2 Polynomials
The Degree of a Polynomial
The Algebra of Polynomials
Zeros and Factorization of Polynomials
The Behavior of a Polynomial Near —1
Graphs of Polynomials
Exercises, Problems, and Wor ked–out Solutions
4.3 Rational Functions
Ratios of Polynomials
The Algebra of Rational Functions
Division of Polynomials
The Behavior of a Rational Function Near —1
Graphs of Rational Functions
Exercises, Problems, and Worked–out Solutions
4.4 Complex Numbers
The Complex Number System
Arithmetic with Complex Numbers
Complex Conjugates and Division of Complex Numbers
Zeros and Factorization of Polynomials, Revisited
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions
5 Exponents and Logarithms
5.1 Exponents and Exponential Functions
Roots
Rational Exponents
Real Exponents
Exponential Functions
Exercises, Problems, and Worked–out Solutions
5.2 Logarithms as Inverses of Exponential Functions
Logarithms Base 2
Logarithms with Any Base
Common Logarithms and the Number of Digits
Logarithm of a Power
Radioactive Decay and Half–Life
Exercises, Problems, and Worked–out Solutions
5.3 Applications of Logarithms
Logarithm of a Product
Logarithm of a Quotient
Earthquakes and the Richter Scale
Sound Intensity and Decibels
Star Brightness and Apparent Magnitude
Change of Base
Exercises, Problems, and Worked–out Solutions
5.4 Exponential Growth
Functions with Exponential Growth
Population Growth
Compound Interest
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions
6 e and the Natural Logarithm
6.1 Defining e and ln
Estimating Area Using Rectangles
Defining e
Defining the Natural Logarithm
Properties of the Exponential Function and ln
Exercises, Problems, and Worked–out Solutions
6.2 Approximations with e and ln
Approximation of the Natural Logarithm
Inequalities with the Natural Logarithm
Approximations with the Exponential Function
An Area Formula
Exercises, Problems, and Worked–out Solutions
6.3 Exponential Growth Revisited
Continuously Compounded Interest
Continuous Growth Rates
Doubling Your Money
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions
7 Trigonometric Functions
7.1 The Unit Circle
The Equation of the Unit Circle
Angles in the Unit Circle
Negative Angles
Angles Greater Than 360—
Length of a Circular Arc
Special Points on the Unit Circle
Exercises, Problems, and Worked–out Solutions
7.2 Radians
A Natural Unit of Measurement for Angles
Negative Angles
Angles Greater Than 2—
Length of a Circular Arc
Area of a Slice
Special Points on the Unit Circle
Exercises, Problems, and Worked–out Solutions
7.3 Cosine and Sine
Definition of Cosine and Sine
Cosine and Sine of Special Angles
The Signs of Cosine and Sine
The Key Equation Connecting Cosine and Sine
The Graphs of Cosine and Sine
Exercises, Problems, and Worked–out Solutions
7.4 More Trigonometric Functions
Definition of Tangent
Tangent of Special Angles
The Sign of Tangent
Connections between Cosine, Sine, and Tangent
The Graph of Tangent
Three More Trigonometric Functions
Exercises, Problems, and Worked–out Solutions
7.5 Trigonometry in Right Triangles
Trigonometric Functions via Right Triangles
Two Sides of a Right Triangle
One Side and One Angle of a Right Triangle
Exercises, Problems, and Worked–out Solutions
7.6 Trigonometric Identities
The Relationship Between Cosine and Sine
Trigonometric Identities for the Negative of an Angle
Trigonometric Identities with
Trigonometric Identities Involving a Multiple of
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions
8 Trigonometric Algebra and Geometry
8.1 Inverse Trigonometric Functions
The Arccosine Function
The Arcsine Function
The Arctangent Function
Exercises, Problems, and Worked–out Solutions
8.2 Inverse Trigonometric Identities
The Arccosine, Arcsine, and Arctangent of
t: Graphical
Approach
The Arccosine, Arcsine, and Arctangent of
t: Algebraic
Approach
Arccosine Plus Arcsine
The Arctangent of 1t
Composition of Trigonometric Functions and Their Inverses
More Compositions with Inverse Trigonometric Functions
Exercises, Problems, and Worked–out Solutions
8.3 Using Trigonometry to Compute Area
The Area of a Triangle via Trigonometry
Ambiguous Angles
The Area of a Parallelogram via Trigonometry
The Area of a Polygon
Exercises, Problems, and Worked–out Solutions
8.4 The Law of Sines and the Law of Cosines
The Law of Sines
Using the Law of Sines
The Law of Cosines
Using the Law of Cosines
When to Use Which Law
Exercises, Problems, and Worked–out Solutions
8.5 Double–Angle and Half–Angle Formulas
The Cosine of 2—
The Sine of 2—
The Tangent of 2—
The Cosine and Sine of —2
The Tangent of —2
Exercises, Problems, and Worked–out Solutions
8.6 Addition and Subtraction Formulas
The Cosine of a Sum and Difference
The Sine of a Sum and Difference
The Tangent of a Sum and Difference
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions
9 Applications of Trigonometry
9.1 Parametric Curves
Curves in the Coordinate Plane
Graphing Inverse Functions as Parametric Curves
Shifting, Stretching, or Flipping a Parametric Curve
Exercises, Problems, and Worked–out Solutions
9.2 Transformations of Trigonometric Functions
Amplitude
Period
Phase Shift
Exercises, Problems, and Worked–out Solutions
9.3 Polar Coordinates
Defining Polar Coordinates
Converting from Polar to Rectangular Coordinates
Converting from Rectangular to Polar Coordinates
Graphs of Polar Equations
Exercises, Problems, and Worked–out Solutions
9.4 Vectors
An Algebraic and Geometric Introduction to Vectors
Vector Addition
Vector Subtraction
The Dot Product
Exercises, Problems, and Worked–out Solutions
9.5 The Complex Plane
Complex Numbers as Points in the Plane
Geometric Interpretation of Complex Multiplication and Division
De Moivre’s Theorem
Finding Complex Roots
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions
10 Systems of Equations and Inequalities
10.1 Equations and Systems of Equations
Solving an Equation
Solving a System of Equations
Systems of Linear Equations
Matrices
Exercises, Problems, and Worked–out Solutions
10.2 Solving Systems of Linear Equations
Gaussian Elimination
Gaussian Elimination with Matrices
Special Cases—No Solutions
Special Cases—Infinitely Many Solutions
Exercises, Problems, and Worked–out Solutions
10.3 Matrix Algebra
Adding and Subtracting Matrices
Multiplying Matrices
The Inverse of a Matrix
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions
11 Sequences, Series, and Limits
11.1 Sequences
Introduction to Sequences
Arithmetic Sequences
Geometric Sequences
Recursively–Defined Sequences
Exercises, Problems, and Worked–out Solutions
11.2 Series
Sums of Sequences
Arithmetic Series
Geometric Series
Summation Notation
The Binomial Theorem
Exercises, Problems, and Worked–out Solutions
11.3 Limits
Introduction to Limits
Infinite Series
Decimals as Infinite Series
Special Infinite Series
Exercises, Problems, and Worked–out Solutions
Chapter Summary and Chapter Review Questions