Pre-Calculus with Trigonometry Book Cover

Pre-Calculus with Trigonometry Book Cover

Pre-Calculus with Trigonometry (Second Edition)

Additional Textbook Resources


TABLE OF CONTENTS

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Chapter 1: Packing Your Suitcase: Tools for Your Journey
Opening 1.OP Chapter Opening
Section 1.1 1.1.1 Finding Functions Using View Tubes
1.1.2 Transformations of Parent Graphs
1.1.3 Basic Inverses and Function Operations
1.1.4 Transformations of Arbitrary Graphs
Section 1.2 1.2.1 Programming Introduction and Point-Slope Form of a Line
1.2.2 Programming Formulas and Experiments
Section 1.3 1.3.1 Solving Non-Right Triangles
1.3.2 Solving Non-Right Triangles, Continued
Section 1.4 1.4.1 Radian as a Unit of Measure
1.4.2 Radians in the Unit Circle
Closure 1.CL Chapter Closure

Chapter 2: Finding the Area Under a Curve
Opening 2.OP Chapter Opening
Section 2.1 2.1.1 Piecewise Functions and an Intuitive Idea of Continuity
2.1.2 Shifting Functions and Periodicity
Section 2.2 2.2.1 Summation and Sigma Notation
2.2.2 Programming a Sum
Section 2.3 2.3.1 Area Under a Curve: Part I
2.3.2 Area Under a Curve: Part II
2.3.3 Area Under a Curve: Part III
2.3.4 Shifting Area
2.3.5 Trapping Area with Trapezoids
2.3.6 Going All to Pieces: Writing an Area Program
2.3.7 Area as a Function
2.3.8 Rocket Launch
Closure 2.CL Chapter Closure

Chapter 3: Exponentials and Logarithms
Opening 3.OP Chapter Opening
Section 3.1 3.1.1 Horizontal and Vertical Stretches
3.1.2 Applications of Exponential Functions
3.1.3 Stretching Exponential Functions
 Section 3.2 3.2.1 Inverses
3.2.2 Logs as Inverse Exponentials
3.2.3 Graphing Log Functions
Section 3.3 3.3.1 Working Within the Law
3.3.2 Solving Exponential Functions and Finding Logs with Bases Other Than Ten
Closure 3.CL Chapter Closure

Chapter 4: Circular Functions
Opening 4.OP Chapter Opening
Section 4.1 4.1.1 Special Angles in the Unit Circle
4.1.2 Sine and Cosine in the Unit Circle
4.1.3 Graphs of Sine and Cosine
4.1.4 Shifts of Sine and Cosine
Section 4.2 4.2.1 Reciprocal Trig Functions and Pythagorean Identities
4.2.2 Simplifying Trig Expressions
4.2.3 Frequency of Sine and Cosine Graphs
4.2.4 Working With Trig Identities
Section 4.3 4.3.1 Applications of Trig Functions
4.3.2 Sine Here and Have Your Parents Cosine
Closure 4.CL Chapter Closure

Chapter 5: Introduction to Limits
Opening 5.OP Chapter Opening
Section 5.1 5.1.1 View Tube With a Twist
5.1.2 Simplifying Rational Functions and Identifying Them as Shifts
5.1.3 Graphing Reciprocals of Functions
Section 5.2 5.2.1 Introduction to Limits
5.2.2 A Different Approach to Limits
5.2.3 Working With One-Sided Limits
5.2.4 More on Limits
5.2.5 Piecewise Functions and Limits
Closure 5.CL Chapter Closure

Chapter 6: Extending Periodic Functions
Opening 6.OP Chapter Opening
Section 6.1 6.1.1 Solving Trig Equations
6.1.2 Inverse Sine and Cosine: Solutions my Calculator Never Told Me
6.1.3 The Ambiguous Case of the Law of Sines
6.1.4 Graphs of Tangent and Inverse Tangent
Section 6.2 6.2.1 Putting all of the Transformations Together
6.2.2 Angle Sum and Difference Formulas
6.2.3 Modeling With Periodic Functions
Section 6.3 6.3.1 Double-Angle Formulas
6.3.2 Solving More Complex Trig Equations
Section 6.4 6.4.1 The Spring Problem
6.4.2 Improving the Spring Problem
Closure 6.CL Chapter Closure

Chapter 7: Algebra for College Mathematics: Problem Solving 101
Opening 7.OP Chapter Opening
Section 7.1 7.1.1 Describing Functions
7.1.2 Describing Functions, Continued
Section 7.2 7.2.1 Setting up Word Problems
7.2.2 Make Your Life Easier by Decomposing Functions
7.2.3 Polynomial Division
7.2.4 Binomial Expansion From Pascal’s Triangle
Section 7.3 7.3.1 Easy Ways to Add Special Series
7.3.2 Geometric Series
7.3.3 Binomial Probabilities
Closure 7.CL Chapter Closure

Chapter 8: More on Limits
Opening 8.OP Chapter Opening
Section 8.1 8.1.1 A Race to Infinity
8.1.2 Limit of Rational Functions
8.1.3 Surprising Rational Functions
8.1.4 Putting the Squeeze on π
Section 8.2 8.2.1 The Number e
8.2.2 Applications of e
8.2.3 Infinite Geometric Series
8.2.4 The Sum of the Harmonic Series
8.2.5 The Fibonacci Sequence
8.2.6 Proof by Induction
Closure 8.CL Chapter Closure

Chapter 9: Rates of Change
Opening 9.OP Chapter Opening
Section 9.1 9.1.1 Rates of Change From Data
9.1.2 More Rates of Change From Data
9.1.3 Slopes and Rates of Change
9.1.4 Average Velocity and Rates of Change
Section 9.2 9.2.1 Moving From AROC to IROC
9.2.2 Secant and Tangent Lines
Closure 9.CL Chapter Closure

Chapter 10: Vectors and Parametric Equations
Opening 10.OP Chapter Opening
Section 10.1 10.1.1 An Introduction to Vectors
10.1.2 Working with Vectors
10.1.3 Applications of Vectors
10.1.4 The Dot Product
Section 10.2 10.2.1 Introduction to Parametric Equations
10.2.2 Graphing Parametric Equations Using a Calculator
10.2.3 Applications of Parametric Equations
Closure 10.CL Chapter Closure

Chapter 11: Polar Equations and Complex Numbers
Opening 11.OP Chapter Opening
Section 11.1 11.1.1 Plotting Polar Coordinates by Hand
11.1.2 Graphs of Polar Equations
11.1.3 Rotating Polar Curves
11.1.4 A Polar Exploration
Section 11.2 11.2.1 Using the Complex Plane
11.2.2 Powers and Roots of Complex Numbers
Closure 11.CL Chapter Closure

Chapter 12: Linear Transformations: Applications of Matrices
Opening 12.OP Chapter Opening
Section 12.1 12.1.1 Basic Operations Using Matrices
12.1.2 Using Matrix Equations to Solve Systems
12.1.3 Applications of Matrices
Section 12.2 12.2.1 Using Matrices to Complete Linear Transformations
12.2.2 Composition of Transformations
12.2.3 Properties of Transformations
Closure 12.CL Chapter Closure

Chapter 13: Conic Sections: Readiness for College Math Text
Opening 13.OP Chapter Opening
Section 13.1 13.1.1 Circles
13.1.2 Ellipses
13.1.3 Hyperbolas
13.1.4 Parabolas
Section 13.2 13.2.1 Second-Degree Equations
Closure 13.CL Chapter Closure

Glossary
Index
 
 

RESOURCE PAGES

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Chapter 1: Packing Your Suitcase: Tools for Your Journey
Chapter 2: Finding the Area Under a Curve
Chapter 3: Exponentials and Logarithms
Chapter 4: Circular Functions
Chapter 5: Introduction to Limits
Chapter 6: Extending Periodic Functions
Chapter 7: Algebra for College Mathematics: Problem Solving 101
Chapter 8: More on Limits
Chapter 9: Rates of Change
Chapter 10: Vectors and Parametric Equations
Chapter 11: Polar Equations and Complex Numbers
Chapter 12: Linear Transformations: Applications of Matrices
Chapter 13: Conic Sections: Readiness for College Math Text

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General eTools
Chapter 1: Packing Your Suitcase: Tools for Your Journey
Chapter 2: Finding the Area Under a Curve
Chapter 3: Exponentials and Logarithms
Chapter 4: Circular Functions
Chapter 5: Introduction to Limits
Chapter 6: Extending Periodic Functions
Chapter 7: Algebra for College Mathematics: Problem Solving 101
Chapter 8: More on Limits
Chapter 9: Rates of Change
Chapter 10: Vectors and Parametric Equations
Chapter 11: Polar Equations and Complex Numbers
Chapter 12: Linear Transformations: Applications of Matrices
Chapter 13: Conic Sections: Readiness for College Math Text

SUPPORT MATERIALS

PCT: Pre-Calculus with Trigonometry: Course Overview PDF
PCT: Pre-Calculus with Trigonometry: Development of Major Content Strands PDF

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