This is the homepage for the free book *Trigonometry*, by Michael Corral
(Schoolcraft College). If you are looking for the *Vector Calculus* homepage, go
here.

You can download the latest version (2016-03-07) of the book *Trigonometry* here:
trigbook.pdf

Current changelog: changelog.txt

The book is a PDF file, which requires a PDF viewer such as the freely available Adobe Acrobat Reader or noncommercial software (e.g. Evince, Okular, xpdf) to view it. The book is distributed under the terms of the GNU Free Documentation License, Version 1.3.

You can buy a printed, bound,
paperback version of the book for $11 plus shipping at the author's storefront on Lulu.com:
http://www.lulu.com/mecmath

Note: While the PDF version hosted here contains full color graphics, the printed version from Lulu.com contains
grayscale graphics in order to minimize the cost of printing.

For those who want to view and/or compile the book's source files, the LaTeX source code is available here:
trigbook-1.2-src.tar.gz

You will need a relatively recent LaTeX installation to compile the source code. In particular, you will need
a recent version of the TikZ graphics package (at least version 2.0), which is available as part of
the TeX Live system, or you can get it here:
http://www.texample.net/tikz/builds/.
A build script (trigbook.sh) for Linux/UNIX systems is included for building the PDF file.
See the included README file for more instructions.

Here is a Java applet showing an application of trigonometry to computer graphics (rotations in the xy-coordinate plane). To use the applet, download the Zip file, extract its contents, then open the rotate2D.html file in your browser. You will need at least version 1.6.0 of the Java plugin.

Numerical code samples: The code samples from the book (written in Java, Python, Octave) can be downloaded here: trigbook_code.zip. These are the programs listed in Section 6.2 of the book.

Go here to see a computer program (in the Tcl programming language) for solving triangles.

Click here for a PDF file showing how to use trigonometric identities to find a simple closed-form expression for sin 18° (and consequently cos 18°), which I prepared for my trigonometry class. Since expressions for sin 15° and cos 15° can be found by using the difference formulas for sine and cosine (with 15° = 45° - 30°), the expressions for sin 18° and cos 18° can then be used again with the difference formulas to get sin 3° and cos 3°, and hence the trigonometric functions of any integer multiple of 3°. Part of the purpose of doing this was to show how useful the product-to-sum formulas are; they do not seem to get the attention they deserve in most textbooks these days - something I wanted to rectify when I wrote my book (where I give a few examples of how those identities are used in physics and electrical engineering).

**Book description**: This is a text on elementary trigonometry, designed for students who
have completed courses in high-school algebra and geometry. Though designed for college students,
it could also be used in high schools. The traditional topics are covered, but a more geometrical
approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving
trigonometric equations) are discussed. A brief tutorial on using Gnuplot to graph trigonometric
functions is included.

There are 495 exercises in the book, with answers and hints to selected exercises.

- Right Triangle Trigonometry
- Angles
- Trigonometric Functions of an Acute Angle
- Applications and Solving Right Triangles
- Trigonometric Functions of Any Angle
- Rotations and Reflections of Angles

- General Triangles
- The Law of Sines
- The Law of Cosines
- The Law of Tangents
- The Area of a Triangle
- Circumscribed and Inscribed Circles

- Identities
- Basic Trigonometric Identities
- Sum and Difference Formulas
- Double-Angle and Half-Angle Formulas
- Other Identities

- Radian Measure
- Radians and Degrees
- Arc Length
- Area of a Sector
- Circular Motion: Linear and Angular Speed

- Graphing and Inverse Functions
- Graphing the Trigonometric Functions
- Properties of Graphs of Trigonometric Functions
- Inverse Trigonometric Functions

- Additional Topics
- Solving Trigonometric Equations
- Numerical Methods in Trigonometry
- Complex Numbers
- Polar Coordinates

- Appendix A: Answers and Hints to Selected Exercises
- Appendix B: Graphing with Gnuplot
- GNU Free Documentation License
- History
- Index

**News**

(2015-07-19) After spending quite a bit of time trying to compile the book correctly with TeX Live 2014 - and not succeeding - I decided to give up and go back to TeX Live 2011. The reason for recompiling was to make a few modifications and corrections. See the changelog for details.

(2012-06-14)
Version 1.2 of *Trigonometry* is now out. The biggest change is the update of the license to
version 1.3 of the GNU Free Documentation License. This was long overdue, and I felt that there
were enough changes in the license to warrant a new version number for the book. I also updated
the Gnuplot tutorial in Appendix B to reflect the current version (4.6.0) of the software, as well
as some stylistic changes. A few typos were corrected and some clarifications made (thanks to Seth
Braver at South Puget Sound Community College for bringing those to my attention).
See the changelog for details.

(2011-11-04) Added a PDF file showing how to find an exact expression for sin 18°. Also made the Java applet for 2-dimensional rotation available again, but this time in a Zip file that can be downloaded, so that the user has to run it locally. Though this site is now on a new hosting provider I am still worried about bandwidth usage, which is why I'm hesitant to have the live applet hosted on the site again.

(2011-08-13)
In addition to being on a new hosting provider, a new update is out. This is primarily
a “maintenance release” to clean up some old
code so that it compiles under TeX Live 2010, which appears to handle fonts
differently than previous versions; in particular the bbding and dingbat font packages
seem a bit buggy (the fonts get substituted, resulting in the wrong
symbols being displayed). So I removed the book's dependence on those packages and
replaced them with the pifont package, which gives a cleaner interface to the
necessary symbols. Similar to the *Vector Calculus* book, some spacing issues also
arose, so those were fixed as well. Additionally, some of the EPS graphics were
improved to have consistent fonts. Lastly, one typo was corrected. See the
changelog for details.

(2011-06-02) Unfortunately I had to remove the applets demonstrating Thales' Theorem and rotations in the xy-coordinate plane. I received a notice from my web hosting provider today that I was exceeding my bandwidth limit, and that my account would be suspended if I did not reduce the bandwidth within seven days. It's possible that the applets are the culprit; I'll find out soon enough.

(2010-12-01) The printed version available at Lulu.com has (finally!) been updated with all the latest corrections. I had been meaning to do this for a while and finally got around to it.

(2010-05-06) The book is now listed on the CLRN Free Digital Textbook Initiative page. This means that the book met the CLRN (California Learning Resource Network) review criteria. Also created a changelog for documenting the updates/corrections to the book.

(2010-04-18) Created a Java applet demonstrating rotations in two dimensions.

(2010-03-28) The book can now be bought as a printed, bound paperback from Lulu.com.

(2010-03-12) Version 1.1 released. The only changes in material are the addition of a section (6.4) on polar coordinates, and a short Sage example was added to Section 6.2.

(2009-08-29) Initial version 1.0 is released.

**Contact**

The author of the book, Michael Corral, can be reached via email at

*Last updated: March 7, 2016*