Trigonometry Tutorials
Trigonometry is the branch of mathematics that studies the relationships between the sides and angles of triangles—especially right-angled triangles. From engineering and physics to navigation and architecture, trigonometry is a foundational skill with real-world applications. Our trigonometry tutorials are designed to break down complex concepts into simple, actionable steps, making trigonometry accessible for students, educators, and anyone looking to refresh their skills.
Whether you’re preparing for exams (SAT, ACT, AP Calculus, or college math), solving real-world problems, or just curious about trigonometry basics, our tutorials cover everything you need to know—from basic ratios to advanced trigonometric identities.
Core Trigonometry Tutorials
There are a few Trigonometry Tutorials
1. Trigonometry Handbook
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 the author 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.
The answers to most of the questions below are inside this handbook, but are seldom taught.
- Is there a method I can learn that will help me recall the key points on a unit circle without memorizing the unit circle?
- What’s the fastest way to graph a Trig function?
- Can I convert the sum of two trig functions to a product of trig functions? How about the other way around, changing a product to a sum?
- Is there an easy way to calculate the area of a triangle if I am given its vertices as points on a Cartesian plane?
- Don’t some of the Polar graphs in Chapter 9 look like they have been drawn with a Spirograph? Why is that?
- A cycloid is both a brachistochrone and a tautochrone. What are these and why are they important? (you will have to look this one up, but it is well worth your time)
- What is a vector cross product and how is it used?
- How do the properties of vectors extend to 3 dimensions, where they really matter?
https://www.mathguy.us/Handbooks/TrigonometryHandbook.pdf
2. Trigonometry Short Course Tutorial
Trigonometry is a branch of mathematics that focuses on relationships between the sides and angles of triangles. The word trigonometry comes from the Latin derivative of Greek words for triangle (trigonon) and measure (metron).
Trigonometry (Trig) is an intricate piece of other branches of mathematics such as, Geometry, lgebra, and Calculus.
In this tutorial we will go over the following topics.
- Understand how angles are measured
- Degrees
- Radians
- Unit circle
- Practice
- Solutions
- Use trig functions to find information about right triangles
- Definition of trig ratios and functions
- Find the value of trig functions given an angle measure
- Find a missing side length given an angle measure
- Find an angle measure using trig functions
- Practice
- Solutions
- Use definitions and fundamental Identities of trig functions
- Fundamental Identities
- Sum and Difference Formulas
- Double and Half Angle Formulas
- Product to Sum Formulas
- Sum to Product Formulas
- Law of Sines and Cosines
- Practice
- Solutions
- Understand key features of graphs of trig functions
- Graph of the sine function
- Graph of the cosine function
- Key features of the sine and cosine function
- Graph of the tangent function
- Key features of the tangent function
- Practice
- Solutions
3. Trigonometry videos
All of the YouTube videos on this page were created and posted by Professor Dave Explains. This series is a thorough approch to mathematics that begins with basic arithmatic and ends with vector calculus. We hope that you find these tutorials useful.
Why Our Trigonometry Tutorials Stand Out
- Step-by-Step Explanations: No jargon—we break down every concept into easy-to-follow steps.
- Real-World Applications: Learn how trigonometry is used in engineering, astronomy, and everyday life.
- Interactive Examples: Visual aids, graphs, and calculators to make learning tangible.
- Free Resources: Downloadable worksheets, cheat sheets (e.g., trig identities cheat sheet), and video tutorials.
Frequently Asked Questions
Q1: What is the easiest way to learn trigonometry?
A1: Start with right triangles and SOHCAHTOA, memorize basic angle values, and practice simple problems daily. Our beginner trigonometry tutorials are designed to make this process painless.
Q2: Do I need a calculator for trigonometry?
A2: For basic angles (0°, 30°, 45°, etc.), you can use exact values, but a calculator is essential for non-standard angles. Our tutorials teach you how to use a calculator correctly for trig functions.
Q3: How is trigonometry used in real life?
A3: Trigonometry is used to calculate heights/distances (surveying), design buildings (architecture), predict tides (oceanography), and even in video game design (3D graphics).
Conclusion
Trigonometry doesn’t have to be intimidating—our trigonometry tutorials are designed to make mastering this essential math skill simple and enjoyable. Whether you’re a student, teacher, or professional, our step-by-step guides, practice problems, and real-world examples will help you build confidence and proficiency in trigonometry.
Start with our beginner tutorials today, and unlock the power of trigonometry!