# Trigonometry

Richard W. Beveridge

Copyright Year: 2014

Publisher: Richard W. Beveridge

Language: English

## Formats Available

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

This textbook is a four-chapter comprehensive collection of Trigonometry topics including right triangle, graphing, identities of Trigonometric functions and Law of sines and cosines. This might be a good practical in-class discussions but has... read more

This textbook is a four-chapter comprehensive collection of Trigonometry topics including right triangle, graphing, identities of Trigonometric functions and Law of sines and cosines. This might be a good practical in-class discussions but has limited explanation to online self-study. There is no or limited discussion on topics of Trigonometric functions in unit circle approach and Inverse Trigonometric functions. The trigonometric functions can be defined in two different but equivalent ways: as functions of real numbers or angles. The two approaches are independent of each other. The author should be explained both approaches because the different approaches are required for different applications. On the other hand, Inverse Trigonometric functions should be discussed thoroughly with the concept of an inverse function with one-to-one relationship.

I did not find any errors or content that was inaccurate, but skipping steps were found in examples.

The author uses 2-3 examples for each section followed by section exercises. There are various real-world applications for each topic. As being Trigonometry is a prerequisite for Calculus, I rather have more direct examples than complicated applications.

In the chapters which are not clearly explained, many examples omitted basic steps. It is somewhat hard to read without well-defined guidelines. The author also uses the acronyms, i.e., sohcahtoa without reasoning.

This text is written systematic ways. Each chapter depends on the previous chapter and they are correlated one after another. The difficult examples are offered gradually increased and consistently presented with application exercises.

The text is divided into sections and chapters that organized well which had flow that is straightforward to follow. But this text overly depends on the graphing calculator i.e., TI-83, computations. Special angles to find exact values and topics of Trigonometric functions in unit circle approach would be inserted after chapter 1.

The organization is fine. All chapters are lineup correctly. There may not be a lot of examples with special angles.

I found no animations, no external links nor graphing calculator demo.

I found no grammatical errors.

The author does not limit the discussion to just real-world applications.

This text will give a brief concept of Trigonometry functions but not in depth. I recommend beginners who wants to learn what Trigonometry functions look alike. I do not recommend students if they want to use this textbook for prepare to move calculus.

This is a text authored in 2014. The material covers Right Triangle Trigonometry (angles, trig ratios, solving right triangles, applications), Graphing the Trigonometric Functions, Trigonometric Identities and Equations, and Law of Sines and Law... read more

This is a text authored in 2014. The material covers Right Triangle Trigonometry (angles, trig ratios, solving right triangles, applications), Graphing the Trigonometric Functions, Trigonometric Identities and Equations, and Law of Sines and Law of Cosines.

There is little formal explanation of the concept of Inverse Trigonometric Functions beyond referencing their existence and accessing them on the TI-83/84 calculator beginning in Solving Right Triangles (1.3). There is no coverage or discussion of the graphs of the inverse trigonometric functions.

There is no coverage of vectors or their applications nor are there any real world applications of radians.

Identities and equations do not include any half-angle relationships. Double angle and sum/difference of two angles are limited to the sine and cosine functions

There is a table of contents covering the basic concepts mentioned above but no glossary or index.

There are no inaccuracies in the text that that could be found.

When working with generating values of the six trigonometric functions, rationalizing the denominator is not mentioned nor is it implemented. Radical values are allowed in denominators which in itself, is not an error but it is inconsistent with the mainstream of textbooks on the market today.

The text covers real world applications that have been covered over and over in texts. The vast majority of the text uses exercises that are not gender or culturally biased. No mention of any personal names or mentions of genders beyond “a man” or “a woman” are present.

The scope of the topics would make it unlikely that this text could be used as a requirement to prepare students for a course in calculus.

The text is not wordy nor is it phrased in a manner that makes it unreadable. There are no innately technical terminologies involved in any application exercises. There are places where the text leaves the reader asking for more detail.

The material is presented in a very linear fashion with each topic building on previous topics. Terminology is consistent and the framework of presentation is appropriate.

The material is presented in a very linear fashion with each topic building on previous topics. The only topic that doesn’t build on previous topics is the presentation of trigonometric graphs. With radian measurement introduced in the first chapter, the chapter on trigonometric graphs could be moved to the end of the text with no loss of continuity.

With the singular missing concept of developing/explaining the inverse trigonometric functions, everything is presented clearly and logically.

There are no real graphics to cause interface issues. There are no links to external material, nor are there any graphic images that can be distorted. Every diagram involving triangles, even in the applications, are “straight line” drawings. This is a strictly “black and white” presentation that doesn’t challenge the imagination.

There were no grammatical errors that were observed. There was one contextual inaccuracy in that a "guy wire" is used to help anchor a tower or pole to prevent it from toppling against the effects of gravity. One exercise has a "guy wire" being placed on the downhill side of a tower where it would be ineffective from an engineering standpoint.

All references to people involve “a man” or “a woman” or “the people” with no names that could be construed to involve or disregard any specific race, ethnicity or culture. It is neither inclusive nor exclusive.

I could not use this text in a university environment. It does not go deep enough into the associated concepts of trigonometry to make it applicable to a student was going to study calculus, physics or engineering. It’s a very basic text and with some additional clarification could be used as an independent study course. I’m not sure it even goes deep enough for a high school trigonometry offering. Used in pieces, it could be used as part of a survey class such as “Topics of Mathematics.”

## 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

## Ancillary Material

## 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.

## About the Contributors

### Author

**Richard W. Beveridge**