Functions, Statistics, and Trigonometry,9780673459268

Functions, Statistics, and Trigonometry

by ; ; ; ; ;
Edition: 2nd
ISBN13: 9780673459268
ISBN10: 0673459268
Format: Hardcover
Pub. Date: 1998-01-01
Publisher(s): SCHOLG
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Table of Contents

Acknowledgments ii
The University of Chicago School Mathematics Project iv
Table of Contents
vi
To the Student 1(3)
Exploring Data
4(76)
Tables and Graphs
6(7)
Stemplots and Dotplots
13(8)
In-class Activity: Using a Statistics Utility to Enter and Analyze Data
19(2)
Measures of Center
21(8)
Quartiles, Percentiles, and Box Plots
29(10)
In-class Activity: Displaying Data with a Statistics Utility
38(1)
Histograms
39(7)
Choosing a Good Display
46(8)
Variance and Standard Deviation
54(8)
Who Wrote The Federalist Papers?
62(18)
Projects
68(2)
Summary and Vocabulary
70(1)
Progress Self-Test
71(2)
Chapter Review
73(7)
Functions and Models
80(78)
The Language of Functions
82(7)
In-class Activity: Linear Regression
88(1)
Linear Models and Correlation
89(8)
The Line of Best Fit
97(8)
Exponential Functions
105(7)
Exponential Models
112(8)
In-class Activity: Using Quadratic Regression
119(1)
Quadratic Models
120(8)
Step Functions
128(6)
Choosing a Good Model
134(7)
The Men's Mile Record
141(17)
Projects
148(2)
Summary and Vocabulary
150(1)
Progress Self-Test
151(1)
Chapter Review
152(6)
Transformations of Graphs and Data
158(72)
Changing Windows
160(7)
The Graph-Translation Theorem
167(6)
Translations of Data
173(6)
Symmetries of Graphs
179(8)
In-class Activity: Functions and Scale Changes
186(1)
The Graph Scale-Change Theorem
187(7)
Scale Changes of Data
194(7)
Composition of Functions
201(7)
Inverse Functions
208(7)
z-Scores
215(15)
Projects
220(2)
Summary and Vocabulary
222(2)
Progress Self-Test
224(1)
Chapter Review
225(5)
Circular Functions
230(78)
Measures of Angles and Rotations
232(7)
Lengths of Arcs and Areas of Sectors
239(6)
In-class Activity: Introducing Sines, Cosines, and Tangents
244(1)
Sines, Cosines, and Tangents
245(6)
Basic Identities Involving Sines, Cosines, and Tangents
251(6)
Exact Values of Sines, Cosines, and Tangents
257(8)
In-class Activity: Graphing Circular Functions
263(2)
The Sine, Cosine, and Tangent Functions
265(7)
Scale-Change Images of Circular Functions
272(6)
Translation Images of Circular Functions
278(7)
The Graph-Standardization Theorem
285(8)
In-class Activity: Daylight in Seattle
292(1)
Modeling with Circular Functions
293(15)
Projects
299(2)
Summary and Vocabulary
301(1)
Progress Self-Test
302(1)
Chapter Review
303(5)
Trigonometric Functions
308(60)
Trigonometric Ratios in Right Triangles
310(6)
The Law of Cosines
316(5)
The Inverse Cosine Function
321(6)
The Law of Sines
327(7)
The Inverse Sine Function
334(6)
The Inverse Tangent Function
340(6)
In-class Activity: Solving Trigonometric Equations Graphically
345(1)
General Solutions to Trigonometric Equations
346(7)
From Washington to Beijing
353(15)
Projects
360(2)
Summary and Vocabulary
362(1)
Progress Self-Test
363(1)
Chapter Review
364(4)
Root, Power, and Logarithm Functions
368(56)
nth Root Functions
370(6)
Rational Power Functions
376(7)
Logarithm Functions
383(7)
In-class Activity: The Number e
389(1)
e and Natural Logarithms
390(8)
In-class Activity: Sums, Differences, and Logarithms
397(1)
Properties of Logarithms
398(5)
Solving Exponential Equations
403(6)
Linearizing Data to Find Models
409(15)
Projects
416(2)
Summary and Vocabulary
418(1)
Progress Self-Test
419(1)
Chapter Review
420(4)
Probability and Simulation
424(62)
Basic Principles of Probability
426(7)
Addition Counting Principles
433(7)
Multiplication Counting Principles
440(5)
Permutations
445(5)
Independent Events
450(7)
Probability Distributions
457(8)
In-class Activity: The Monty Hall Problem
464(1)
Designing Simulations
465(6)
Simulations with Technology
471(15)
Projects
478(2)
Summary and Vocabulary
480(1)
Progress Self-Test
481(1)
Chapter Review
482(4)
Sequences, Series, and Combinations
486(68)
Formulas for Sequences
488(8)
Limits of Sequences
496(7)
Arithmetic Series
503(6)
Geometric Series
509(7)
In-class Activity: Exploring Infinite Series
515(1)
Infinite Series
516(7)
Combinations
523(6)
Pascal's Triangle
529(6)
The Binomial Theorem
535(5)
Binomial Probabilities
540(14)
Projects
546(2)
Summary and Vocabulary
548(2)
Progress Self-Test
550(1)
Chapter Review
551(3)
Polynomial Functions
554(72)
Polynomial Models
556(8)
In-class Activity: Finding Some Key Points of a Polynomial Function
563(1)
Graphs of Polynomial Functions
564(6)
Finding Polynomial Models
570(7)
Division and the Remainder Theorem
577(7)
The Factor Theorem
584(6)
Complex Numbers
590(6)
The Fundamental Theorem of Algebra
596(7)
Factoring Sums and Differences of Powers
603(5)
Advanced Factoring Techniques
608(4)
Roots and Coefficients of Polynomials
612(14)
Projects
617(2)
Summary and Vocabulary
619(2)
Progress Self-Test
621(1)
Chapter Review
622(4)
Binomial and Normal Distributions
626(70)
Binomial Probability Distributions
628(6)
Mean and Standard Deviation of a Binomial Distribution
634(7)
Is That Coin Fair?
641(8)
In-class Activity: The Graph of y = e-x2
648(1)
Normal Curves
649(5)
Finding Probabilities Using the Standard Normal Distribution
654(8)
Other Normal Distributions
662(9)
In-class Activity: The Sampling Distribution of the Mean
670(1)
Sampling Distributions and the Central Limit Theorem
671(9)
Confidence and Cautions in Statistical Reasoning
680(16)
Projects
687(2)
Summary and Vocabulary
689(2)
Progress Self-Test
691(1)
Chapter Review
692(4)
Matrices and Trigonometry
696(56)
Matrix Multiplication
698(6)
Matrices for Transformations
704(6)
Matrices for Composites of Transformations
710(6)
The General Rotation Matrix
716(5)
Formulas for cos (α + β) and sin (α + β)
721(5)
Formulas for cos 2&thetas; and sin 2&thetas;
726(5)
Inverses of 2 x 2 Matrices
731(7)
Matrices in Computer Graphics
738(14)
Projects
745(2)
Summary and Vocabulary
747(1)
Progress Self-Test
748(1)
Chapter Review
749(3)
Quadratic Relations
752(52)
The Geometry of the Ellipse
754(6)
The Algebra of the Ellipse
760(8)
The Hyperbola
768(8)
Rotating Relations
776(8)
The General Quadratic Equation
784(8)
It's All Done with Mirrors
792(12)
Projects
797(2)
Summary and Vocabulary
799(2)
Progress Self-Test
801(1)
Chapter Review
802(2)
Further Work with Trigonometry
804(62)
The Secant, Cosecant, and Cotangent Functions
806(5)
Proving Trigonometric Identities
811(5)
Restrictions on Identities
816(4)
Polar Coordinates
820(7)
Polar Graphs
827(6)
The Geometry of Complex Numbers
833(6)
In-class Activity: Geometric Transformations Using Complex Multiplication
838(1)
Trigonometric Form of Complex Numbers
839(7)
DeMoivre's Theorem
846(6)
The Mandelbrot Set
852(14)
Projects
858(2)
Summary and Vocabulary
860(2)
Progress Self-Test
862(1)
Chapter Review
863(3)
Appendix A: Parent Functions and Graphs 866(5)
Appendix B: Programming Languages 871(3)
Appendix C: Random Number Table 874(1)
Appendix D: Standard Normal Distribution Table 875(1)
Selected Answers 876(35)
Glossary 911(13)
Index 924(10)
List of Symbols 934(1)
Photo Acknowledgments 935

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