We have tried to make this edition of Trigonometry useful to students in a variety of programs. For example, students who have encountered elements of triangle trig in previous courses may be able to skip all or part of Chapters 1 through 3. Students preparing for technical courses may not need much of the material after Chapter 6 or 7. Chapters 9 and 10 cover vectors and polar coordinates, optional topics that occur in some trigonometry courses but are often reserved for precalculus.

This book covers the major topics within the study of trigonometry, including vectors and their applications. At the University of Minnesota, this material is 75% of the PreCalculus II course, with the remaining 25% of that course covering algebraic topics which are included in a separate text. It comprises approximately 10-12 weeks worth of material at the college level; a typical college student would spend about 120 hours total learning this material.

Trigonometry’ derives from the Greek, meaning literally ‘triangle measuring’. Because ‘trigonometry’ is such a long word, people often informally abbreviate it as ‘trig’. The tools developed in trigonometry complement and expand those developed in geometry. For example, geometry's ‘ASA’ (angle-side-angle) congruence theorem states that a unique triangle is formed by two angles and the included side. But what are the lengths (measures) of those remaining two sides? Trigonometry gives the answer. Trigonometry is used heavily in calculus (e.g., related rate problems and integration techniques), which is why it comprises a large part of any precalculus course.Trigonometry is used in astronomy, navigation, architecture and land-surveying. The trigonometric functions are invaluable in studying any periodic (repetitive) phenomena. Love your cell phone and music CDs? Signal processing, noise cancellation, and music coding all use trigonometry.

Since these notes grew as a supplement to a textbook, the majority of the problems in the supplemental problems (of which there are several for almost every lecture) are more challenging and less routine than would normally be found in a book of trigonometry (note there are several inexpensive problem books available for trigonometry to help supplement the text of this book if you find the problems lacking in number). Most of the problems will give key insights into new ideas and so you are encouraged to do as many as possible by yourself before going for help.

Trigonometry is useful. If you would like to learn a bit about trigonometry, or brush up on it, then read on. These notes are more of an introduction and guide than a full course. For a full course you should take a class or at least read a book. There are no grades and no tests for you to take, and no transcripts and no awards. There are a few exercises for you to work on, but only a few. The exercises are the most important aspect of a trigonometry course, or any course in mathematics for that matter.

This Trigonometry Handbook was developed primarily through work with a number of High
School and College Trigonometry classes. In addition, a number of more advanced topics have
been added to the handbook to whet the student’s appetite for higher level study.
One of the main reasons why I wrote this handbook was to encourage the student to wonder;
to ask “what about …” or “what if …”. I find that students are so busy today that they don’t
have the time, or don’t take the time, to seek out the beauty and majesty that exists in
Mathematics. And, it is there, just below the surface. So be curious and go find it.

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The calculators on this site were grouped into 4 sections: financial, fitness & health, math, and others. All of the calculators were developed in-house. Some calculators use open-source JavaScript components under different open-source licenses. More than 90% of the calculators are based on well-known formulas or equations from textbooks, such as the mortgage calculator, BMI calculator, etc. If formulas are controversial, we provide the results of all popular formulas, as can be seen in the Ideal Weight Calculator. Calculators such as the love calculator that are solely meant for amusement are based on internal formulas. The results of the financial calculators were reviewed by our financial advisors, who work for major personal financial advising firms. The results of the health calculators were reviewed and approved by local medical doctors. More than 99% of the descriptive content was developed in-house with a small amount of content taken from wikipedia.org under the GNU Free Documentation License. The descriptive content of the financial calculators was created and reviewed by our financial team. The descriptive content of the health calculators was reviewed by local medical doctors.

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Trigonometry starts on Chapter 7 as it is the 2nd half of MATH 1113, Precalculus. Bullet points without links are works-in-progress.

Content is based on College Trigonometry, 3rd Corrected Edition by Carl Stitz and
Jeffrey Zeager, to whom we are grateful beyond words for their dedication in
creating and sharing their OER textbook.
This textbook has been developed by Ruth Trygstad, Salt Lake Community
College (SLCC), with contributions from Shawna Haider (SLCC), Spencer
Bartholomew (SLCC) and Maggie Cummings (University of Utah). Many
additional faculty and staff from both Salt Lake Community College and the
University of Utah have helped with this pilot edition. The project has been
sponsored and supported by SLCC, the SLCC Math Department and the University
of Utah Math Department. Special thanks goes to Jason Pickavance, Suzanne
Mozdy and Peter Trapa for their encouragement.
Additional content, including Exercises, has been borrowed from OpenStax
College, Algebra and Trigonometry, openstaxcollege.org/textbooks/college-
algebra-and-trigonometry

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.