Ted Sundstrom, Grand Valley State University
Steven Schlicker, Grand Valley State University
Pub Date: 2016
Publisher: Grand Valley State University
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This text was created for a three-credit trigonometry course (MATH123-Trigonometry) at Grand Valley State University. Other than conic sections, the read more
This text was created for a three-credit trigonometry course (MATH123-Trigonometry) at Grand Valley State University. Other than conic sections, the text covers everything that is typically included in a first trigonometry course. However, the comprehensiveness of this text exceeds other texts in many important ways. Trigonometric concepts are developed in a very thorough, patient and coherent manner that most certainly speaks to students, while developing their mathematical understanding and analytical thinking. It takes the time to engage the reader in the thought process using links to well developed and integrated diagrams, Geogrebra applets, worksheets, and YouTube screencast videos (developed by Grand Valley State University). The beginning review activities, focus questions, progress checks, and sections summaries provide direction and support active and deep learning. Answers and hints to selected exercise and geometric facts about circles and triangles are included in the Appendices. This text takes a very interesting reverse chronological approach to trigonometry. Trigonometric functions are introduced as circular functions and later as trigonometric functions. I am now convinced that this provides a more holistic perspective of trigonometry and better clarifies many concepts such as the dimensionless nature of radians.
I did not note any errors or bias in the content of the book.
The textbook begins with the most relevant applications of trigonometry, but is not written in a manner that will require necessary updates. If needed, it could be easily updated. The author's invite feedback, especially from students using the text.
The text makes even the most complex of the trigonometric concepts clear and accessible to students. It develops concepts and the definitions of terminology so that students can both understand and remember them. It includes progress checks for students to check their understanding. Section summaries list important definitions and results proven in the section. The disciplined and motivated student could learn trigonometry from this text on their own. Some students may need further clarification of the reading.
The text is internally consistent in terms of terminology and framework. Each of the beginning activities reviews prior mathematical work necessary for the new section. The answers to these beginning activities are developed in the material later in the section. Each section has progress checks with answers to these checks in Appendix A. Each section is summarized listing important definitions and results proven in the section.
This text is best read from the beginning to the end to fully understand how ideas are developed. However, each chapter can stand on its own. Each reading section is fairly small and the text within each section is broken up into small chunks to keep the reader engaged, active, and interested.
This text is very organized, well structured, and flows very well. It is particularly strong in its clear and logical development of topics. There is the right amount of rhythm and variety to keep the reader engaged. It uses language that is more conversational and approachable than most mathematical texts.
There were a few links to figures that did not seems to take me exactly to the figure, but at least close to them. Otherwise, I did not note any interface issues, navigation problems, distortion of images, or any other distracting or confusing display features.
I noted only a couple of grammatical errors in Progress Check 1.2 and on page 168 where a word or two seemed to be missing.
This text is not culturally insensitive in any way. Rather the variety of resources and beginning activities engage students with different learning styles and mathematical backgrounds.
I think this text is excellent. It uses a guided approach and has a conversational, interesting, and engaging tone that promises to effectively reach all learners from the serious math student to those with math anxiety. I will definitely make this text available to my students to get their feedback and hope to use it as the main text in the future. It could greatly facilitate teaching and learning both in online and traditional courses.
Table of Contents
- Note to Students
- The Trigonometric Functions
- Graphs of the Trigonometric Functions
- Triangles and Vectors
- Trigonometric Identities and Equations
- Complex Numbers and Polar Coordinates
- Appendix A: Answers for the Progress Checks
- Appendix B: Answers and Hints for Selected Exercises
- Appendix C: Some Geometric Facts about Triangles and Parallelograms
About the Book
This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged.
Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section. Each section also contains several progress checks that are short exercises or activities designed to help readers determine if they are understanding the material. In addition, the text contains links to several interactive Geogebra applets or worksheets. These applets are usually part of a beginning activity or a progress check and are intended to be used as part of the textbook.
About the Contributors
Ted Sundstrom is a mathematics professor at Grand Valley State University in Allendale, MI.
Steven Schlicker is a mathematics professor at Grand Valley State University in Allendale, MI.