Trigonometry: Student Edition

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  • Edition: 6th
  • Format: Hardcover
  • Publisher: Prentice Hall (School Division)
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This book, intended for a graphing calculator optional trigonometry course, offers students the content and tools they will need to successfully master trigonometry. The authors have addressed the needs of students who will continue their study of mathematics, as well as those who are taking trigonometry as their final mathematics course. Emphasis is placed on exploring mathematical concepts by using real date, current applications and optional technology. Applied examples and exercises, allowing students to focus on real-life applications of mathematics. Selected examples feature traditional algebraic as well as optional graphing calculator solutions. We have taken great care to only use this format in examples where the graphing calculator can naturally be used to support and/or enhance the algebraic solution. For those interested in Mathematics.

Table of Contents

Prefacep. viii
Supplements Guidep. xii
Trigonometric Functionsp. 1
Anglesp. 2
Basic Terminology
Degree Measure
Standard Position
Coterminal Angles
Angle Relationships and Similar Trianglesp. 9
Geometric Properties
Trigonometric Functionsp. 20
Trigonometric Functions
Quadrantal Angles
Using the Definitions of the Trigonometric Functionsp. 27
Reciprocal Identities
Signs and Ranges of Function Values
Pythagorean Identities
Quotient Identities
Summaryp. 37
Review Exercisesp. 39
Testp. 42
Quantitative Reasoningp. 44
Acute Angles and Right Trianglesp. 45
Trigonometric Functions of Acute Anglesp. 46
Right-Triangle-Based Definitions of the Trigonometric Functions
Trigonometric Function Values of Special Angles
Trigonometric Functions of Non-Acute Anglesp. 55
Reference Angles
Special Angles as Reference Angles
Finding Angle Measures with Special Angles
Finding Trigonometric Function Values Using a Calculatorp. 62
Finding Function Values Using a Calculator
Finding Angle Measures Using a Calculator
Solving Right Trianglesp. 68
Significant Digits
Solving Triangles
Angles of Elevation or Depression
Further Applications of Right Trianglesp. 77
Further Applications
Summaryp. 86
Review Exercisesp. 88
Testp. 91
Quantitative Reasoningp. 92
Radian Measure and Circular Functionsp. 93
Radian Measurep. 94
Radian Measure
Converting Between Degrees and Radians
Finding Function Values for Angles in Radians
Applications of Radian Measurep. 99
Arc Length on a Circle
Area of a Sector of a Circle
The Unit Circle and Circular Functionsp. 108
Circular Functions
Finding Values of Circular Functions
Determining a Number with a Given Circular Function Value
Applying Circular Functions
Linear and Angular Speedp. 116
Linear Speed
Angular Speed
Summaryp. 122
Review Exercisesp. 124
Testp. 128
Quantitative Reasoningp. 129
Graphs of the Circular Functionsp. 131
Graphs of the Sine and Cosine Functionsp. 132
Periodic Functions
Graph of the Sine Function
Graph of the Cosine Function
Graphing Techniques, Amplitude, and Period
Using a Trigonometric Model
Translations of the Graphs of the Sine and Cosine Functionsp. 146
Horizontal Translations
Vertical Translations
Combinations of Translations
Determining a Trigonometric Model Using Curve Fitting
Graphs of the Other Circular Functionsp. 155
Graphs of the Cosecant and Secant Functions
Graphs of the Tangent and Cotangent Functions
Addition of Ordinates
Summary Exercises on Graphing Circular Functionsp. 168
Harmonic Motionp. 168
Simple Harmonic Motion
Damped Oscillatory Motion
Summaryp. 173
Review Exercisesp. 175
Testp. 178
Quantitative Reasoningp. 779
Trigonometric Identitiesp. 181
Fundamental Identitiesp. 182
Negative-Angle Identities
Fundamental Identities
Using the Fundamental Identities
Verifying Trigonometric Identitiesp. 188
Verifying Identities by Working with One Side
Verifying Identities by Working with Both Sides
Sum and Difference Identities for Cosinep. 197
Difference Identity for Cosine
Sum Identity for Cosine
Cofunction Identities
Applying the Sum and Difference Identities
Sum and Difference Identities for Sine and Tangentp. 205
Sum and Difference Identities for Sine
Sum and Difference Identities for Tangent
Applying the Sum and Difference Identities
Double-Angle Identitiesp. 212
Double-Angle Identities
Product-to-Sum and Sum-to-Product Identities
Half-Angle Identitiesp. 221
Half-Angle Identities
Applying the Half-Angle Identities
Summary Exercises on Verifying Trigonometric Identitiesp. 227
Summaryp. 229
Review Exercisesp. 231
Testp. 233
Quantitative Reasoningp. 234
Inverse Circular Functions and Trigonometric Equationsp. 235
Inverse Circular Functionsp. 236
Inverse Functions
Inverse Sine Function
Inverse Cosine Function
Inverse Tangent Function
Remaining Inverse Circular Functions
Inverse Function Values
Trigonometric Equations Ip. 249
Solving by Linear Methods
Solving by Factoring
Solving by Quadratic Methods
Solving by Using Trigonometric Identities
Trigonometric Equations IIp. 256
Equations with Half-Angles
Equations with Multiple Angles
Equations Involving Inverse Trigonometric Functionsp. 262
Solving for x in Terms of y Using Inverse Functions
Solving Inverse Trigonometric Equations
Summaryp. 269
Review Exercisesp. 271
Testp. 273
Quantitative Reasoningp. 274
Applications of Trigonometry and Vectorsp. 275
Oblique Triangles and the Law of Sinesp. 276
Congruency and Oblique Triangles
Derivation of the Law of Sines
Solving SAA and ASA Triangles (Case 1)
Area of a Triangle
The Ambiguous Case of the Law of Sinesp. 287
Description of the Ambiguous Case
Solving SSA Triangles (Case 2)
Analyzing Data for Possible Number of Triangles
The Law of Cosinesp. 293
Derivation of the Law of Cosines
Solving SAS and SSS Triangles (Cases 3 and 4)
Heron's Formula for the Area of a Triangle
Vectors, Operations, and the Dot Productp. 305
Basic Terminology
Algebraic Interpretation of Vectors
Operations with Vectors
Dot Product and the Angle Between Vectors
Applications of Vectorsp. 315
The Equilibrant
Incline Applications
Navigation Applications
Summaryp. 322
Review Exercisesp. 325
Testp. 329
Quantitative Reasoningp. 330
Complex Numbers, Polar Equations, and Parametric Equationsp. 331
Complex Numbersp. 332
Basic Concepts of Complex Numbers
Complex Solutions of Equations
Operations on Complex Numbers
Trigonometric (Polar) Form of Complex Numbersp. 341
The Complex Plane and Vector Representation
Trigonometric (Polar) Form
Converting Between Trigonometric and Polar Forms
An Application of Complex Numbers to Fractals
The Product and Quotient Theoremsp. 347
Products of Complex Numbers in Trigonometric Form
Quotients of Complex Numbers in Trigonometric Form
De Moivre's Theorem; Powers and Roots of Complex Numbersp. 352
Powers of Complex Numbers (De Moivre's Theorem)
Roots of Complex Numbers
Polar Equations and Graphsp. 359
Polar Coordinate System
Graphs of Polar Equations
Converting from Polar to Rectangular Equations
Classifying Polar Equations
Parametric Equations, Graphs, and Applicationsp. 371
Basic Concepts
Parametric Graphs and Their Rectangular Equivalents
The Cycloid
Applications of Parametric Equations
Summaryp. 379
Review Exercisesp. 382
Testp. 385
Quantitative Reasoningp. 386
Exponential and Logarithmic Functionsp. 387
Exponential Functionsp. 388
Exponents and Properties
Exponential Functions
Exponential Equations
Compound Interest
The Number e and Continuous Compounding
Exponential Models and Curve Fitting
Logarithmic Functionsp. 402
Logarithmic Equations
Logarithmic Functions
Properties of Logarithms
Evaluating Logarithms; Equations and Applicationsp. 413
Common Logarithms
Natural Logarithms
Logarithms to Other Bases
Exponential and Logarithmic Equations
Summaryp. 426
Review Exercisesp. 428
Testp. 431
Quantitative Reasoningp. 432
Equations and Inequalitiesp. 433
Solving Linear Equations
Solving Quadratic Equations
Solving Linear Inequalities
Interval Notation
Three-Part Inequalities
Graphs of Equationsp. 442
The Rectangular Coordinate System
The Pythagorean Theorem and the Distance Formula
The Midpoint Formula
Graphing Equations
Functionsp. 450
Relations and Functions
Domain and Range
Determining Whether a Relation Is a Function
Function Notation
Increasing, Decreasing, and Constant Functions
Graphing Techniquesp. 460
Stretching and Shrinking
Glossaryp. 469
Solutions to Selected Exercisesp. S-1
Answers to Selected Exercisesp. A-1
Index of Applicationsp. I-1
Indexp. I-3
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