Course Title: Trigonometry
Course Description: Trigonometry is a branch of mathematics that focuses on the study of angles, triangles, and trigonometric functions. This course provides students with a deep understanding of trigonometry and its practical applications in real-world scenarios. It serves as a foundation for advanced mathematics courses.
Course Objectives: By the end of this course, students should be able to:
- Understand the fundamental concepts of trigonometry, including angles, triangles, and unit circles.
- Solve trigonometric equations and inequalities.
- Apply trigonometric functions (sine, cosine, tangent) to solve problems involving right triangles.
- Work with the trigonometric identities and the Pythagorean identities.
- Graph trigonometric functions and understand their properties.
- Solve problems involving oblique triangles.
- Explore applications of trigonometry in various fields, such as physics, engineering, and navigation.
- Develop critical thinking and problem-solving skills.
Textbook:
- [Insert Trigonometry Textbook Title and Author(s)]
Materials:
- Notebook or binder for class notes and assignments.
- Scientific calculator with trigonometric functions (if allowed).
- Pencils, erasers, and a ruler.
Grading:
- Homework/Classwork: XX%
- Quizzes: XX%
- Tests: XX%
- Projects: XX%
- Final Exam: XX%
Course Outline:
Unit 1: Introduction to Trigonometry
- Basics of angles and measurement.
- Introduction to trigonometric functions.
- Unit circle and radian measure.
Unit 2: Right Triangle Trigonometry
- Trigonometric ratios (sine, cosine, tangent).
- Solving right triangles.
- Applications of right triangle trigonometry.
Unit 3: Trigonometric Functions and Graphs
- Graphing trigonometric functions.
- Amplitude, period, and phase shift.
- Inverse trigonometric functions.
Unit 4: Trigonometric Identities
- Fundamental trigonometric identities.
- Pythagorean identities.
- Verifying and simplifying trigonometric expressions.
Unit 5: Laws of Sines and Cosines
- Solving oblique triangles.
- Law of Sines.
- Law of Cosines.
Unit 6: Trigonometric Equations and Applications
- Solving trigonometric equations.
- Applications of trigonometry in real-world problems.
- Review and preparation for final exam.
Note: This is a general example of a high school Trigonometry syllabus. It’s essential to adapt it to meet the specific needs and standards of your school or district. The percentages for grading, the textbook, and materials may vary. Additionally, consult with your school’s curriculum guidelines and any state or district standards that may apply.
Free Textbooks
You can find free trigonometry textbooks and resources online from various reputable sources. Here are a few options for free trigonometry textbooks:
- CK-12 Trigonometry:
- CK-12 offers a comprehensive trigonometry textbook that covers a wide range of trigonometric topics, including interactive lessons, practice problems, and quizzes.
- Website: https://www.ck12.org/book/ck-12-trigonometry/
- OpenStax Precalculus:
- OpenStax provides a free, peer-reviewed “Precalculus” textbook that includes comprehensive coverage of trigonometric concepts and functions.
- Website: https://openstax.org/details/books/precalculus
- Paul’s Online Math Notes – Trigonometry:
- Paul’s Online Math Notes offers free notes and tutorials on trigonometry topics, including explanations and example problems.
- Website: http://tutorial.math.lamar.edu/Classes/Alg/Trig.aspx
- Purplemath:
- Purplemath provides free lessons and tutorials on various trigonometry topics. While not a full textbook, it’s a valuable resource for learning and understanding trigonometric concepts.
- Website: https://www.purplemath.com/modules/index.htm
- Textbook Revolution:
- Textbook Revolution is a resource dedicated to the free distribution of textbooks and educational materials. You can search for free trigonometry textbooks and related resources.
- Website: http://textbookrevolution.org/
These resources offer a variety of formats, including interactive online lessons, PDFs, and downloadable materials. Be sure to explore these options and choose the one that aligns with your learning preferences and needs. Always check the licensing terms and usage policies for each resource to ensure that you are using them legally and responsibly.
MOOCs
As of my last knowledge update in January 2022, trigonometry courses may be offered as part of broader mathematics or precalculus courses on MOOC platforms. While you may not find standalone “trigonometry” courses, you can explore precalculus courses that cover trigonometric topics. Please keep in mind that course offerings on MOOC platforms can change over time, so it’s a good idea to check the current course listings. Here are some MOOC platforms where you can often find relevant courses:
- Coursera:
- Coursera offers precalculus courses that include trigonometry topics. Some of these courses may offer free access to course materials, with the option to pay for a certificate.
- Website: https://www.coursera.org/
- edX:
- edX provides precalculus courses that cover trigonometry. As with Coursera, you may have the option to audit courses for free or pay for a verified certificate.
- Website: https://www.edx.org/
- Khan Academy:
- Khan Academy offers a comprehensive set of free math courses, including precalculus, which covers trigonometry concepts.
- Website: https://www.khanacademy.org/
- MIT OpenCourseWare (OCW):
- MIT OCW provides free access to course materials from Massachusetts Institute of Technology (MIT) courses, including precalculus topics that involve trigonometry.
- Website: https://ocw.mit.edu/index.htm
- Harvard Online Courses (HarvardX):
- Harvard University offers precalculus courses through their HarvardX program on edX, covering trigonometric concepts.
- Website: https://online-learning.harvard.edu/catalog?keywords=precalculus
- FutureLearn:
- FutureLearn offers math courses that include precalculus topics, such as trigonometry. Some courses provide free access to content, while certificates may be available for a fee.
- Website: https://www.futurelearn.com/subjects/mathematics-and-stats-courses/precalculus
While these courses may not be explicitly labeled as “trigonometry” courses, they often cover trigonometric functions, identities, and applications as part of their precalculus curriculum. Be sure to explore the course descriptions to find the specific topics you’re interested in.