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Trigonometry

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Richard W. Beveridge

Pub Date: 2014

Publisher: Independent

Language: English

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CC BY-NC-SA

Table of Contents

1. Right Triangle Trigonometry

  • 1.1 Measuring Angles
  • 1.2 The Trigonometric Ratios
  • 1.3 Solving Triangles
  • 1.4 Applications
  • 1.5 More Applications

2. Graphing the Trigonometric Functions

  • 2.1 Trigonometric Functions of Non-Acute Angles
  • 2.2 Graphing Trigonometric Functions
  • 2.3 The Vertical Shift of a Trigonometric Function
  • 2.4 Phase Shift
  • 2.5 Combining the Transformations

3. Trigonometric Identities and Equations

  • 3.1 Reciprocal and Pythagorean Identities
  • 3.2 Double-Angle Identities
  • 3.3 Trigonometric Equations
  • 3.4 More Trigonometric Equations

4. The Law of Sines; The Law of Cosines

  • 4.1 The Law of Sines
  • 4.2 The Law of Sines: the ambiguous case
  • 4.3 The Law of Cosines
  • 4.4 Applications

About the Book

The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky. Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry - the relationship between angles and distances.

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Richard W. Beveridge