Trigonometry: Student Edition

by Schneider; Lial; ornsby

• ISBN13: 9780321047830
• ISBN10: 0321047834
• Edition: 6th
• Format: Hardcover
• Publisher: Prentice Hall (School Division)

Summary

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

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