Investigating College Algebra and Trigonometry with Technology with Trigonometry Chapters 12 and 13 Student CD-Rom and Access Code Card
1st Edition
Published on 16. July 2008
Book
Hardback
698 pages
978-0-470-41332-6 (ISBN)
Description
Technology and an investigative pedagogy are powerful tools for
fostering in-depth understanding of mathematics concepts.
Investigating College Algebra and Trigonometry with
Technology presents the core concepts of College Algebra and
Trigonometry within a technology-oriented, data-driven, applied
framework that embraces investigative, collaborative
learning. With this text, students use graphing
calculators, and optionally Microsoft (R) Excel and other
technologies, to explore patterns and to make, test, and generalize
conjectures. Most importantly, investigations?which engage
students in analysis of real-world data?promote collaboration
and bring relevance to the mathematics students are learning.
The American Mathematical Association of Two-Year Colleges
(AMATYC) and the Mathematical Association of America?s
Committee on Undergraduate Programs in Mathematics (CUPM) set
standards for meaningful and relevant mathematics and the
refocusing of the College Algebra and Trigonometry course. This
text follows their recommendations for using technology,
experiencing varied applications of mathematics, and having
opportunities to solve problems, reason critically, exhibit
persistence, and test conjectures through investigations and data
analysis.
fostering in-depth understanding of mathematics concepts.
Investigating College Algebra and Trigonometry with
Technology presents the core concepts of College Algebra and
Trigonometry within a technology-oriented, data-driven, applied
framework that embraces investigative, collaborative
learning. With this text, students use graphing
calculators, and optionally Microsoft (R) Excel and other
technologies, to explore patterns and to make, test, and generalize
conjectures. Most importantly, investigations?which engage
students in analysis of real-world data?promote collaboration
and bring relevance to the mathematics students are learning.
The American Mathematical Association of Two-Year Colleges
(AMATYC) and the Mathematical Association of America?s
Committee on Undergraduate Programs in Mathematics (CUPM) set
standards for meaningful and relevant mathematics and the
refocusing of the College Algebra and Trigonometry course. This
text follows their recommendations for using technology,
experiencing varied applications of mathematics, and having
opportunities to solve problems, reason critically, exhibit
persistence, and test conjectures through investigations and data
analysis.
More details
Language
English
Place of publication
Chichester
United Kingdom
Publishing group
John Wiley and Sons Ltd
Target group
College/higher education
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 264 mm
Width: 225 mm
Thickness: 39 mm
Weight
1858 gr
ISBN-13
978-0-470-41332-6 (9780470413326)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Content
Annotated Contents vii
Preface xix
To the Student xxvii
To the Instructor xxix
Acknowledgments xxxi
Chapter 1: Problem Solving 1
1.1 Pictures, Graphs, and Diagrams 2
1.2 Symbolic Representation 9
1.3 Organizing Information 16
1.4 Measures of Central Tendency and Box Plots 24
1.5 Measures of Spread 31
Chapter 1 Review 45
Chapter 2: Patterns and Recursion 53
2.1 Recursively Defined Sequences 54
2.2 Modeling Growth and Decay 64
2.3 A First Look at Limits 71
2.4 Graphing and Sequences 77
2.5 Loans and Investments 86
Chapter 2 Review 99
Chapter 3: Linear Models and Systems 103
3.1 Linear Equations 104
3.2 Revisiting Slope 111
3.3 Fitting a Line to Data 119
3.4 Linear Systems 127
3.5 Substitution and Elimination 133
Chapter 3 Review 142
Chapter 4: Functions, Relations, and Transformations 148
4.1 Interpreting Graphs 149
4.2 Function Notation 155
4.3 Lines in Motion 163
4.4 Translations and the Quadratic Family 170
4.5 Reflections and the Square Root Family 177
4.6 Stretches and Shrinks and the Absolute Value Family 184
4.7 Transformations and the Circle Family 192
4.8 Compositions of Functions 200
Chapter 4 Review 211
Chapter 5: Exponential, Power, and Logarithmic Functions 215
5.1 The Exponential Function 216
5.2 Properties of Exponents 223
5.3 Fractional Exponents and Roots 229
5.4 Applications of Power Equations 239
5.5 Building Inverses of Functions 243
5.6 The Logarithmic Function 251
5.7 Properties of Logarithms 257
5.8 Applications of Logarithms 264
Chapter 5 Review 273
Chapter 6: Quadratic and Other Polynomial Functions 277
6.1 Polynomial Degree and Finite Differences 278
6.2 Equivalent Quadratic Forms 286
6.3 Completing the Square 294
6.4 The Quadratic Formula 301
6.5 Complex Numbers 307
6.6 Factoring Polynomials 314
6.7 Higher-Degree Polynomials 320
6.8 More about Finding Solutions 327
Chapter 6 Review 337
Chapter 7: Matrices and Linear Systems 341
7.1 Matrix Representations 342
7.2 Matrix Operations 349
7.3 The Row Reduction Method 360
7.4 Solving Systems with Inverse Matrices 368
7.5 Systems of Linear Inequalities 378
7.6 Linear Programming 385
Chapter 7 Review 395
Chapter 8: Parametric Equations and Trigonometry 401
8.1 Graphing Parametric Equations 402
8.2 Converting Parametric to Nonparametric Equations 411
8.3 Right Triangle Trigonometry 418
8.4 Using Trigonometry to Set a Course 431
8.5 Projectile Motion 438
8.6 The Law of Sines 445
8.7 The Law of Cosines 453
Chapter 8 Review 462
Chapter 9: Conic Sections and Rational Functions 466
9.1 Using the Distance Formula 467
9.2 Circles and Ellipses 474
9.3 Parabolas 486
9.4 The Hyperbola 494
9.5 Nonlinear Systems of Equations 503
9.6 Introduction to Rational Functions 508
9.7 Graphs of Rational Functions 516
9.8 Operations with Rational Expressions 524
Chapter 9 Review 533
Chapter 10: Series 539
10.1 Arithmetic Series 540
10.2 Infinite Geometric Series 547
10.3 Partial Sums of Geometric Series 554
Chapter 10 Review 562
Chapter 11: Probability 565
11.1 Randomness and Probability 566
11.2 Counting Outcomes and Tree Diagrams 577
11.3 Mutually Exclusive Events and Venn Diagrams 586
11.4 Random Variables and Expected Value 593
11.5 Permutations and Probability 600
11.6 Combinations and Probability 607
11.7 The Binomial Theorem and Pascal?s Triangle 613
Chapter 11 Review 623
Chapter 12: Trigonometric Functions (on the Student CD)
12.1 Defining the Circular Function
12.2 Radian Measure and Arc Length
12.3 Graphing Trigonometric Functions
12.4 Inverses of Trigonometric Functions
12.5 Polar Coordinates
Chapter 13: Trigonometric Identities (on the Student CD)
13.1 Fundamental Trigonometric Identities
13.2 Sum and Difference Identities
13.3 Double- and Half-Angle Identities
13.4 Modeling with Trigonometric Equations
13.5 Solving Trigonometric Equations
Chapter 13 Review
Selected Answers 627
Glossary 675
Photo Credits 687
Index 688
Resources on the Student CD
Prerequisite Review: Numbers and Figures ? Operations on
Numbers ?
The Ideas that Motivate Algebra ? Exponents ? Radicals
? Polynomials ?
Factoring Polynomials ? Rational Expressions
Chapter 12 Trigonometric Functions
Chapter 13 Trigonometric Identities
Calculator Notes
Microsoft (R) Excel Notes
Interactive Spreadsheets for Excel Explorations
Preface xix
To the Student xxvii
To the Instructor xxix
Acknowledgments xxxi
Chapter 1: Problem Solving 1
1.1 Pictures, Graphs, and Diagrams 2
1.2 Symbolic Representation 9
1.3 Organizing Information 16
1.4 Measures of Central Tendency and Box Plots 24
1.5 Measures of Spread 31
Chapter 1 Review 45
Chapter 2: Patterns and Recursion 53
2.1 Recursively Defined Sequences 54
2.2 Modeling Growth and Decay 64
2.3 A First Look at Limits 71
2.4 Graphing and Sequences 77
2.5 Loans and Investments 86
Chapter 2 Review 99
Chapter 3: Linear Models and Systems 103
3.1 Linear Equations 104
3.2 Revisiting Slope 111
3.3 Fitting a Line to Data 119
3.4 Linear Systems 127
3.5 Substitution and Elimination 133
Chapter 3 Review 142
Chapter 4: Functions, Relations, and Transformations 148
4.1 Interpreting Graphs 149
4.2 Function Notation 155
4.3 Lines in Motion 163
4.4 Translations and the Quadratic Family 170
4.5 Reflections and the Square Root Family 177
4.6 Stretches and Shrinks and the Absolute Value Family 184
4.7 Transformations and the Circle Family 192
4.8 Compositions of Functions 200
Chapter 4 Review 211
Chapter 5: Exponential, Power, and Logarithmic Functions 215
5.1 The Exponential Function 216
5.2 Properties of Exponents 223
5.3 Fractional Exponents and Roots 229
5.4 Applications of Power Equations 239
5.5 Building Inverses of Functions 243
5.6 The Logarithmic Function 251
5.7 Properties of Logarithms 257
5.8 Applications of Logarithms 264
Chapter 5 Review 273
Chapter 6: Quadratic and Other Polynomial Functions 277
6.1 Polynomial Degree and Finite Differences 278
6.2 Equivalent Quadratic Forms 286
6.3 Completing the Square 294
6.4 The Quadratic Formula 301
6.5 Complex Numbers 307
6.6 Factoring Polynomials 314
6.7 Higher-Degree Polynomials 320
6.8 More about Finding Solutions 327
Chapter 6 Review 337
Chapter 7: Matrices and Linear Systems 341
7.1 Matrix Representations 342
7.2 Matrix Operations 349
7.3 The Row Reduction Method 360
7.4 Solving Systems with Inverse Matrices 368
7.5 Systems of Linear Inequalities 378
7.6 Linear Programming 385
Chapter 7 Review 395
Chapter 8: Parametric Equations and Trigonometry 401
8.1 Graphing Parametric Equations 402
8.2 Converting Parametric to Nonparametric Equations 411
8.3 Right Triangle Trigonometry 418
8.4 Using Trigonometry to Set a Course 431
8.5 Projectile Motion 438
8.6 The Law of Sines 445
8.7 The Law of Cosines 453
Chapter 8 Review 462
Chapter 9: Conic Sections and Rational Functions 466
9.1 Using the Distance Formula 467
9.2 Circles and Ellipses 474
9.3 Parabolas 486
9.4 The Hyperbola 494
9.5 Nonlinear Systems of Equations 503
9.6 Introduction to Rational Functions 508
9.7 Graphs of Rational Functions 516
9.8 Operations with Rational Expressions 524
Chapter 9 Review 533
Chapter 10: Series 539
10.1 Arithmetic Series 540
10.2 Infinite Geometric Series 547
10.3 Partial Sums of Geometric Series 554
Chapter 10 Review 562
Chapter 11: Probability 565
11.1 Randomness and Probability 566
11.2 Counting Outcomes and Tree Diagrams 577
11.3 Mutually Exclusive Events and Venn Diagrams 586
11.4 Random Variables and Expected Value 593
11.5 Permutations and Probability 600
11.6 Combinations and Probability 607
11.7 The Binomial Theorem and Pascal?s Triangle 613
Chapter 11 Review 623
Chapter 12: Trigonometric Functions (on the Student CD)
12.1 Defining the Circular Function
12.2 Radian Measure and Arc Length
12.3 Graphing Trigonometric Functions
12.4 Inverses of Trigonometric Functions
12.5 Polar Coordinates
Chapter 13: Trigonometric Identities (on the Student CD)
13.1 Fundamental Trigonometric Identities
13.2 Sum and Difference Identities
13.3 Double- and Half-Angle Identities
13.4 Modeling with Trigonometric Equations
13.5 Solving Trigonometric Equations
Chapter 13 Review
Selected Answers 627
Glossary 675
Photo Credits 687
Index 688
Resources on the Student CD
Prerequisite Review: Numbers and Figures ? Operations on
Numbers ?
The Ideas that Motivate Algebra ? Exponents ? Radicals
? Polynomials ?
Factoring Polynomials ? Rational Expressions
Chapter 12 Trigonometric Functions
Chapter 13 Trigonometric Identities
Calculator Notes
Microsoft (R) Excel Notes
Interactive Spreadsheets for Excel Explorations