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Trigonometry

ISBN: 9780321245434 | 0321245431
Edition: 8th
Format: Hardcover
Publisher: PRENTICE HALL SCHOOL GROUP
Pub. Date: 6/2/2004

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SummaryTable of Contents
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.
Prefaceviii
Supplements Guidexii
Trigonometric Functions
1(44)
Angles
2... MORE
Basic Terminology
Degree Measure
Standard Position
Coterminal Angles
Angle Relationships and Similar Triangles
9(11)
Geometric Properties
Triangles
Trigonometric Functions
20(7)
Trigonometric Functions
Quadrantal Angles
Using the Definitions of the Trigonometric Functions
27(18)
Reciprocal Identities
Signs and Ranges of Function Values
Pythagorean Identities
Quotient Identities
Summary
37(2)
Review Exercises
39(3)
Test
42(2)
Quantitative Reasoning
44(1)
Acute Angles and Right Triangles
45(48)
Trigonometric Functions of Acute Angles
46(9)
Right-Triangle-Based Definitions of the Trigonometric Functions
Cofunctions
Trigonometric Function Values of Special Angles
Trigonometric Functions of Non-Acute Angles
55(7)
Reference Angles
Special Angles as Reference Angles
Finding Angle Measures with Special Angles
Finding Trigonometric Function Values Using a Calculator
62(6)
Finding Function Values Using a Calculator
Finding Angle Measures Using a Calculator
Solving Right Triangles
68(9)
Significant Digits
Solving Triangles
Angles of Elevation or Depression
Further Applications of Right Triangles
77(16)
Bearing
Further Applications
Summary
86(2)
Review Exercises
88(3)
Test
91(1)
Quantitative Reasoning
92(1)
Radian Measure and Circular Functions
93(38)
Radian Measure
94(5)
Radian Measure
Converting Between Degrees and Radians
Finding Function Values for Angles in Radians
Applications of Radian Measure
99(9)
Arc Length on a Circle
Area of a Sector of a Circle
The Unit Circle and Circular Functions
108(8)
Circular Functions
Finding Values of Circular Functions
Determining a Number with a Given Circular Function Value
Applying Circular Functions
Linear and Angular Speed
116(15)
Linear Speed
Angular Speed
Summary
122(2)
Review Exercises
124(4)
Test
128(1)
Quantitative Reasoning
129(2)
Graphs of the Circular Functions
131(50)
Graphs of the Sine and Cosine Functions
132(14)
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
146(9)
Horizontal Translations
Vertical Translations
Combinations of Translations
Determining a Trigonometric Model Using Curve Fitting
Graphs of the Other Circular Functions
155(13)
Graphs of the Cosecant and Secant Functions
Graphs of the Tangent and Cotangent Functions
Addition of Ordinates
Summary Exercises on Graphing Circular Functions
168(1)
Harmonic Motion
168(13)
Simple Harmonic Motion
Damped Oscillatory Motion
Summary
173(2)
Review Exercises
175(3)
Test
178(1)
Quantitative Reasoning
179(2)
Trigonometric Identities
181(54)
Fundamental Identities
182(6)
Negative-Angle Identities
Fundamental Identities
Using the Fundamental Identities
Verifying Trigonometric Identities
188(9)
Verifying Identities by Working with One Side
Verifying Identities by Working with Both Sides
Sum and Difference Identities for Cosine
197(8)
Difference Identity for Cosine
Sum Identity for Cosine
Cofunction Identities
Applying the Sum and Difference Identities
Sum and Difference Identities for Sine and Tangent
205(7)
Sum and Difference Identities for Sine
Sum and Difference Identities for Tangent
Applying the Sum and Difference Identities
Double-Angle Identities
212(9)
Double-Angle Identities
Product-to-Sum and Sum-to-Product Identities
Half-Angle Identities
221(14)
Half-Angle Identities
Applying the Half-Angle Identities
Summary Exercises on Verifying Trigonometric Identities
227(2)
Summary
229(2)
Review Exercises
231(2)
Test
233(1)
Quantitative Reasoning
234(1)
Inverse Circular Functions and Trigonometric Equations
235(40)
Inverse Circular Functions
236(13)
Inverse Functions
Inverse Sine Function
Inverse Cosine Function
Inverse Tangent Function
Remaining Inverse Circular Functions
Inverse Function Values
Trigonometric Equations I
249(7)
Solving by Linear Methods
Solving by Factoring
Solving by Quadratic Methods
Solving by Using Trigonometric Identities
Trigonometric Equations II
256(6)
Equations with Half-Angles
Equations with Multiple Angles
Equations Involving Inverse Trigonometric Functions
262(13)
Solving for x in Terms of y Using Inverse Functions
Solving Inverse Trigonometric Equations
Summary
269(2)
Review Exercises
271(2)
Test
273(1)
Quantitative Reasoning
274(1)
Applications of Trigonometry and Vectors
275(56)
Oblique Triangles and the Law of Sines
276(11)
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
287(6)
Description of the Ambiguous Case
Solving SSA Triangles (Case 2)
Analyzing Data for Possible Number of Triangles
The Law of Cosines
293(12)
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
305(10)
Basic Terminology
Algebraic Interpretation of Vectors
Operations with Vectors
Dot Product and the Angle Between Vectors
Applications of Vectors
315(16)
The Equilibrant
Incline Applications
Navigation Applications
Summary
322(3)
Review Exercises
325(4)
Test
329(1)
Quantitative Reasoning
330(1)
Complex Numbers, Polar Equations, and Parametric Equations
331(56)
Complex Numbers
332(9)
Basic Concepts of Complex Numbers
Complex Solutions of Equations
Operations on Complex Numbers
Trigonometric (Polar) Form of Complex Numbers
341(6)
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
347(5)
Products of Complex Numbers in Trigonometric Form
Quotients of Complex Numbers in Trigonometric Form
De Moivre's Theorem; Powers and Roots of Complex Numbers
352(7)
Powers of Complex Numbers (De Moivre's Theorem)
Roots of Complex Numbers
Polar Equations and Graphs
359(12)
Polar Coordinate System
Graphs of Polar Equations
Converting from Polar to Rectangular Equations
Classifying Polar Equations
Parametric Equations, Graphs, and Applications
371(16)
Basic Concepts
Parametric Graphs and Their Rectangular Equivalents
The Cycloid
Applications of Parametric Equations
Summary
379(3)
Review Exercises
382(3)
Test
385(1)
Quantitative Reasoning
386(1)
Exponential and Logarithmic Functions
387(82)
Exponential Functions
388(14)
Exponents and Properties
Exponential Functions
Exponential Equations
Compound Interest
The Number e and Continuous Compounding
Exponential Models and Curve Fitting
Logarithmic Functions
402(11)
Logarithms
Logarithmic Equations
Logarithmic Functions
Properties of Logarithms
Evaluating Logarithms; Equations and Applications
413(20)
Common Logarithms
Natural Logarithms
Logarithms to Other Bases
Exponential and Logarithmic Equations
Summary
426(2)
Review Exercises
428(3)
Test
431(1)
Quantitative Reasoning
432(1)
Appendix A Equations and Inequalities
433(9)
Equations
Solving Linear Equations
Solving Quadratic Equations
Inequalities
Solving Linear Inequalities
Interval Notation
Three-Part Inequalities
Appendix B Graphs of Equations
442(8)
The Rectangular Coordinate System
The Pythagorean Theorem and the Distance Formula
The Midpoint Formula
Graphing Equations
Circles
Appendix C Functions
450(10)
Relations and Functions
Domain and Range
Determining Whether a Relation Is a Function
Function Notation
Increasing, Decreasing, and Constant Functions
Appendix D Graphing Techniques
460(9)
Stretching and Shrinking
Reflecting
Symmetry
Translations
Glossary469
Solutions to Selected Exercises1(1)
Answers to Selected Exercises1(1)
Index of Applications1(2)
Index3


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