Master Math : Trigonometry

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Title:

Master Math : Trigonometry

Author:

Ross, Debra.

ISBN:

9781598639858

Personal Author:

Ross, Debra.

Edition:

2nd edition.

Publication Date:

2009

Publication Information:

Cengage Learning, Inc, 2009.

Physical Description:

420p : illustrations : 680gm.

Abstract:

A trigonometry guide that explains the subject matter in a user-friendly manner. It provides step-by-step solutions for things you need to know about the subject including trigonometric functions, inverse trigonometric functions, trigonometric identities, equations and inequalities, vectors, polar coordinates, and more.

Copies:

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Shelf Number

516.24

Material Type

Reference book

Item Barcode

30116017705573

Status

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Bound With These Titles

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Summary

Get ready to master the fundamentals of trigonometry! Master Math: Trigonometry is a comprehensive reference guide that explains and clarifies the principles oftrigonometry in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics, including a review of basic geometry, and progressingthrough to the more advanced topics, the book helps clarify trigonometry using step-by-step procedures and solutions, along with examples and applications. A complete table of contents and a comprehensive index enable you to quickly find specific topics, and the approachable style and format facilitate an understandingof what can be intimidating and tricky skills. Perfect for both students who need some extra help or rusty professionals who want to brush up, Master Math: Trigonometry will help you master everything from identities and circular functions to solving triangles and trigonometric equations.

Introduction	p. 1
Chapter 1 Review of Numbers and Coordinate Systems	p. 3
1.1 Review of Numbers, Including Natural, Whole, Integers, Zero, Rational, Irrational, Real, Complex, and Imaginary Numbers	p. 3
1.2 Absolute Value	p. 7
1.3 Significant Digits and Rounding Numbers and Decimals	p. 7
1.4 Review of Coordinate Systems, Including Two- and Three-Dimensional Rectangular Coordinates, Polar Coordinates, Cylindrical Coordinates, and Spherical Coordinates	p. 9
1.5 Chapter 1 Summary and Highlights	p. 14
Chapter 2 Review of Geometry	p. 17
2.1 Introduction	p. 17
2.2 Lines and Angles	p. 19
2.3 Triangles	p. 23
2.4 Polygons and Quadrilaterals	p. 28
2.5 Conic Sections, Including Circles, Arcs and Angles, Ellipses, Parabolas, and Hyperbolas	p. 31
2.6 Three-Dimensional Objects, Including Cubes, Rectangular Solids, Cylinders, Spheres, Cones, and Pyramids	p. 45
2.7 Chapter 2 Summary and Highlights	p. 48
Chapter 3 Triangles and Trigonometric Functions	p. 49
3.1 Right Triangles and the Trigonometric Functions	p. 49
3.2 Solving Right Triangles	p. 54
3.3 Examples and Applications of Right Triangles	p. 55
3.4 Oblique Triangles and the Law of Sines and Law of Cosines	p. 62
3.5 Solving Oblique Triangles	p. 67
3.6 Examples and Applications of Oblique Triangles	p. 72
3.7 Finding the Area of a Triangle	p. 77
3.8 Chapter 3 Summary and Highlights	p. 87
Chapter 4 Trigonometric Functions in a Coordinate System and Circular Functions	p. 91
4.1 Review of Functions and Their Properties	p. 92
4.2 Types of Functions, Including Composite, Inverse, Linear, Nonlinear, Even, Odd, Exponential, Logarithmic, Identity, Absolute Value, Squaring, Cubing, Square Root, Cube Root, Reciprocal, and Functions with More Than One Variable	p. 94
4.3 Coordinate Systems, Radians, Degrees, and Arc Length	p. 103
4.4 Angles in Standard Position and Coterminal Angles	p. 107
4.5 The Trigonometric Functions Defined in a Coordinate System in Standard Position, Quadrant Signs, and Quadrantal Angles	p. 108
4.6 Reference Angles and Reference Triangles	p. 112
4.7 Negative Angles	p. 118
4.8 Reciprocal Functions and Cofunction Relationships	p. 119
4.9 Circular Functions and the Unit Circle	p. 120
4.10 Linear and Angular Velocity	p. 125
4.11 Chapter 4 Summary and Highlights	p. 128
Chapter 5 Graphs of Trigonometric and Circular Functions and Their Periodic Nature	p. 131
5.1 Circular Motion	p. 131
5.2 Graphs of Sine and Cosine	p. 137
5.3 Transforming Graphs of Sine and Cosine Through Changes in Amplitude, Period, and Vertical and Horizontal Shifting	p. 144
5.4 Applications of Sinusoids	p. 157
5.5 Graphs of Secant and Cosecant	p. 164
5.6 Graphs of Tangent and Cotangent	p. 169
5.7 Chapter 5 Summary and Highlights	p. 173
Chapter 6 Inverse Trigonometric Functions	p. 177
6.1 Review of General Inverse Functions	p. 177
6.2 Inverse Trigonometric Functions	p. 183
6.3 Inverse Sine and Inverse Cosine	p. 188
6.4 Inverse Tangent	p. 197
6.5 Inverse Cotangent, Inverse Secant, and Inverse Cosecant	p. 204
6.6 Chapter 6 Summary and Highlights	p. 214
Chapter 7 Trigonometric Identities	p. 217
7.1 Summary of Identities	p. 217
7.2 Quotient Identities and Reciprocal Identities	p. 220
7.3 Pythagorean Identities	p. 220
7.4 Negative Number/Angle Identities	p. 222
7.5 Verifying Trigonometric Identities	p. 225
7.6 Sum and Difference of Angles/Numbers Identities, Also Called Addition and Subtraction Identities	p. 228
7.7 Cofunction Identities	p. 234
7.8 Supplementary Angle Relations	p. 237
7.9 Double-Angle/Number Identities	p. 238
7.10 Half-Angle Identities	p. 243
7.11 Product-To-Sum Identities	p. 246
7.12 Sum/Difference-To-Product Identities	p. 248
7.13 Squared Formulas	p. 252
7.14 Chapter 7 Summary and Highlights	p. 253
Chapter 8 Trigonometric Functions in Equations and Inequalities	p. 257
8.1 Review of Solving Algebraic Equations	p. 257
8.2 Review of Solving Algebraic Quadratic Equations	p. 262
8.3 Review of Solving Algebraic Inequalities	p. 269
8.4 Solving Algebraic Equations and Inequalities Using Graphing	p. 270
8.5 Introduction to Solving Trigonometric Equations and Inequalities	p. 273
8.6 Solving Simple Trigonometric Equations Using Standard Position Angles, Reference Triangles, and Identities	p. 274
8.7 Solving Trigonometric Equations Involving Powers Using Factoring, a Unit Circle, and Identities	p. 276
8.8 Solving Trigonometric Equations and Inequalities Using the Quadratic Formula, Identities, Unit Circles, Factoring, and Graphing	p. 281
8.9 Estimating Solutions to Trigonometric Equations and Inequalities Using Graphing	p. 287
8.10 Chapter 8 Summary and Highlights	p. 290
Chapter 9 Trigonometric Functions and Vectors	p. 293
9.1 Definitions of Vectors	p. 293
9.2 Representing Vectors in Terms of Their Components in a Coordinate System	p. 295
9.3 Representing Vectors in Terms of Their Components in a Coordinate System Using the Unit Vectors i, j, and k	p. 298
9.4 Addition and Subtraction of Vectors	p. 300
9.5 Simple Vector Problems	p. 304
9.6 Multiplying a Vector with a Scalar	p. 309
9.7 Dot or Scalar Products	p. 310
9.8 Vector or Cross Product	p. 314
9.9 Chapter 9 Summary and Highlights	p. 318
Chapter 10 Trigonometric Functions in Polar Coordinates and Equations, and Parametric Equations	p. 321
10.1 Polar Coordinates Defined	p. 321
10.2 Converting Between Rectangular and Polar Coordinate Systems and Equations	p. 325
10.3 Graphing Polar Equations	p. 332
10.4 Parametric Equations	p. 342
10.5 Chapter 10 Summary and Highlights	p. 353
Chapter 11 Complex Numbers and the Complex Plane	p. 355
11.1 Complex Numbers Defined	p. 355
11.2 The Complex Plane in Rectangular Form	p. 358
11.3 Addition and Subtraction of Complex Numbers in Rectangular Form	p. 359
11.4 Complex Numbers in Polar Form and the Complex Plane	p. 360
11.5 Converting Between Rectangular and Polar Form	p. 362
11.6 Multiplication and Division of Complex Numbers in Rectangular and Polar Forms	p. 364
11.7 Powers and Roots of Complex Numbers	p. 372
11.8 Chapter 11 Summary and Highlights	p. 378
Chapter 12 Relationships Between Trigonometric Functions, Exponential Functions, Hyperbolic Functions, and Series Expansions	p. 381
12.1 Relationships Between Trigonometric and Exponential Functions	p. 381
12.2 Background: Summary of Sequences, Progressions, and Series, and Expanding a Function into a Series	p. 383
12.3 Hyperbolic Functions	p. 389
12.4 Chapter 12 Summary and Highlights	p. 393
Chapter 13 Spherical Trigonometry	p. 395
13.1 Definitions and Properties	p. 395
13.2 Measuring Spherical Triangles	p. 399
13.3 The Law of Sines and the Law of Cosines for Spherical Triangles for Calculating Sides and Angles	p. 400
13.4 Celestial Sphere	p. 405
13.5 Chapter 13 Summary and Highlights	p. 407
Index	p. 409

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Master Math : Trigonometry

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