Trigonometric relations involve trigonometric functions. There is an awful amount of trigonometric identities. The most basic one is the Pythagorean theorem expressed in terms of sine and cosine:.
Calculate trignometric equations, prove identities and evaluate functions step-by-step
And, of course, no list of trigonometric relations could be complete unless the Laws of Cosines and Sines are mentioned. Trigonometry is a methodology for finding some unknown elements of a triangle or other geometric shapes provided the data includes a sufficient amount of linear and angular measurements to define a shape uniquely. For example, two sides a and b of a triangle and the angle they include define the triangle uniquely. The latter can be used to find the circumradius. Contact Front page Contents Up.
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If you are listening to these videos on headphones, you may want to consider setting your sound channels to come through both sides. This document will give you an idea of how to accomplish that. 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.
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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.
Trigonometry - Open Textbook Library
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. 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. 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.
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Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor.