Easy Way Series: E-Z Trigonometry

Editor/Author Downing, Douglas
Publication Year: 2010
Publisher: Barron's Educational Series

Price: Core Collection Only
ISBN: 978-0-76-414251-2
Category: Mathematics & Statistics - Mathematics
Book Status: Available
Table of Contents

E-Z Trigonometry explains angles and triangles, and demonstrates the solutions to right triangle problems.

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Table of Contents

  • Acknowledgments
  • Introduction
  • 1. Angles and Triangles
  • The Rainstorm
  • Measuring Angles
  • The Raging River Flood
  • Triangles to the Rescue
  • Complete Guide to Triangles
  • Notes to Chapter 1
  • Exercises
  • 2. Solving Right Triangle Problems
  • The Height of the Tree
  • Calculating Heights with Similar Triangles
  • The New Ski Jump
  • The Shifting Star
  • The Distance to the Star
  • Notes to Chapter 2
  • Exercises
  • 3. Trigonometric Functions: sin, cos, and tan
  • Too Many Triangles
  • The Gremlin's Vile Threat
  • The Holiday Lighting Display
  • 30-60-90 Triangles
  • The Decorative Adjustable Triangle
  • The Sine Ratio
  • The Tangent Ratio
  • Functions
  • Definition of Trigonometric Functions
  • Notes to Chapter 3
  • Exercises
  • 4. Applications of Trigonometric Functions
  • The Balloon Ride
  • Velocity Vectors
  • Component Vectors
  • * The Off-Course River Boat
  • * The Message-Delivering System
  • * The Distance of Travel of the Capsule
  • * The Slippery Slope
  • * Friction
  • * The Maximum Angle of Tilt
  • * The Merry-Go-Round Streamers
  • * Centrifugal Force
  • Note to Chapter 4
  • Exercises
  • 5. Radian Measure
  • Recordis Writes Out the Table
  • sin 90°
  • sin 0°
  • The Attack of the Killer Bees
  • Measuring Rotations
  • Radian Measure
  • The Special Number π
  • Converting Radians to Degrees
  • Coterminal Angles
  • The Shifting Sun
  • The Radius of the Earth
  • Trigonometric Functions
  • Cofunctions
  • Cotangent Function
  • Reciprocal Functions
  • The Secant and Cosecant Functions
  • Notes to Chapter 5
  • Exercises
  • 6. Trigonometric Identities
  • Pythagorean Identities
  • Addition Rules
  • Double-Angle Rules
  • Trigonometric Identities
  • Note to Chapter 6
  • Exercises
  • 7. Law of Cosines and Law of Sines
  • The Triangle with the Unknown Parts
  • Law of Cosines
  • Law of Sines
  • Exercises
  • 8. Graphs of Trigonometric Functions
  • The Bouncing Wagon
  • The Periodic Function
  • The Graph of the Sine Function
  • The Graph of the Cosine Function
  • Graphs of the Tangent and Cotangent Functions
  • Graphs of the Secant and Cosecant Functions
  • Alternating Current
  • Amplitude
  • Frequency
  • Phase
  • Solving an Equation with a Graphing Calculator
  • Exercises
  • 9. Waves
  • * The Waves on the Lake
  • * Wavelength
  • * Harmonic Waves
  • * Sound Waves
  • * Adding Sine Functions of Different Frequencies
  • * Standing Waves in Guitar Strings
  • * Music
  • The Threat of the Terrible Flood
  • Note to Chapter 9
  • Exercises
  • 10. Inverse Trigonometric Functions
  • Pal's Pet Pigeons to the Rescue
  • Inverse Functions
  • The Arctan, Arcsin, and Arccos Functions
  • Principal Values
  • Graphs of Inverse Trigonometric Functions
  • Exercises
  • 11. Polar Coordinates
  • The Pigeon Messenger Service
  • Rectangular Coordinates
  • Polar Coordinates
  • Equations in Polar Coordinates
  • Exercises
  • 12. Complex Numbers
  • * The Imaginary Number i
  • * Properties of Complex Numbers
  • * Polar Coordinate Form of Complex Numbers
  • * Multiplying Complex Numbers
  • * Powers of Complex Numbers
  • * Roots of Complex Numbers
  • Notes to Chapter 12
  • Exercises
  • 13. Coordinate Rotation and Conic Sections
  • * The Peaceful Bay Town-Planning Problem
  • * Rotated Coordinate Systems
  • * The New Improved Pigeon-Aiming System
  • * Rotations in Polar Coordinates
  • * Rotations in Rectangular Coordinates
  • * The Two-Unknown Quadratic Equation
  • * Circles
  • * Ellipses
  • * Parabolas
  • * Hyperbolas
  • * Conic Sections
  • * Translation of Axes
  • * The Pesky xy Term
  • * The Perplexing Parabola with the Tilted Axis
  • * The Rotated Equation
  • * The Solution of a Second-Degree Two-Unknown Equation
  • * The Graph of the Tilted Ellipse
  • * The Discriminant
  • Three-Dimensional Rotations and Virtual Reality
  • Note to Chapter 13
  • Exercises
  • 14. Spherical Trigonometry
  • * Mysterious Triangles and Riddles
  • * Great Circles and Small Circles
  • * Latitude and Longitude
  • * Spherical Triangles
  • * Spherical Right Triangles
  • * Sailing Along the Shortest Course
  • * Law of Sines and Law of Cosines
  • * The Altitude of the Sun at the Beach
  • * The Celestial Sphere
  • * The Lost Assistant at the Unknown Latitude
  • * Solving Spherical Triangles
  • Notes to Chapter 14
  • Exercises
  • 15. Polynomial Approximation for sin x and cos x
  • * The Quest for the Elusive Algebraic Expression
  • * The Infinite-Degree Polynomial
  • * The Factorial Function
  • * Series Representation of sin x and cos x
  • Exercises
  • Answers to Exercises
  • Appendix
  • Significant Digits
  • Computer Spreadsheets
  • Summary of Trigonometric Formulas
  • Stars (•) mark topics and exercises that are more difficult or that require more background knowledge.