Trigonometry is a fundamental branch of mathematics that plays a crucial role in high school and college math courses, as well as fields like physics, engineering, and computer science. Whether you’re just starting your journey in trigonometry or preparing for an exam, my Trigonometry and Precalculus Video Series provides clear explanations, problem-solving techniques, and free guided notes to help you succeed.

Why Mastering Trigonometry and Precalculus is Essential

Understanding trigonometry and precalculus is essential for solving real-world problems in geometry, physics, and calculus. Concepts like trigonometric functions, identities, equations, inverse functions, and polynomial functions are key building blocks for success in advanced mathematics and STEM careers.

What You’ll Learn in This Course

This video series covers the essential topics in trigonometry and precalculus with detailed step-by-step explanations and worked-out examples. By following along with the videos and utilizing the free guided notes, you can reinforce your learning and build confidence in solving complex mathematical problems.

1. Basic Trigonometric and Precalculus Concepts

• Types of angles: acute, right, obtuse, straight, and reflex

• Degrees and radians: definitions and conversions

• Coterminal angles and standard position

• Arc length and sector area formulas

• Triangle classification and similar triangles in applications

• Functions, domain and range, and transformations

2. Right Triangle Trigonometry

• The Pythagorean Theorem

• Trigonometric functions: sine, cosine, tangent, and reciprocals

• 45-45-90 and 30-60-90 triangles

• Solving right triangles

3. Trigonometric Functions

• Unit circle introduction and how to memorize it

• Trigonometric functions of real numbers

• Reference angles and special angle evaluations

• Signs of trigonometric functions and exact values

4. Graphing Trigonometric and Precalculus Functions

• Graphing sine, cosine, and sinusoidal functions

• Tangent, cosecant, secant, and cotangent graphs

• Graphing polynomial, rational, exponential, and logarithmic functions

• Real-world applications (e.g., Ferris wheel equations)

5. Inverse Trigonometric Functions

• Understanding inverses and the horizontal line test

• Evaluating and graphing inverse trigonometric functions

• Solving composite trigonometric expressions

6. Trigonometric Identities

• Complete list of identities: Pythagorean, even/odd, periodicity

• Sum & difference, product-to-sum, and double angle formulas

• How to simplify trigonometric expressions

• Step-by-step identity verification

7. Solving Trigonometric Equations

• Solving basic and multi-angle trigonometric equations

• Factoring and quadratic trigonometric equations

• Using identities to solve trigonometric equations

8. Advanced Topics in Trigonometry and Precalculus

• Triangle congruence theorems: SSS, SAS, ASA, AAS, HL

• Law of Sines and Law of Cosines (including the ambiguous case)

• Heron’s Formula and area of a triangle

• Polar coordinates, graphing, and conversions

• Parametric equations and plane curves

• Complex numbers in polar form and De Moivre’s Theorem

• Sequences, series, and limits

Follow Along with Free Guided Notes

To help you retain key concepts and formulas, I’ve created structured guided notes that you can download for free. These notes will help you:

• Organize essential formulas and theorems

• Work through step-by-step examples

• Strengthen your understanding with practice problems

👉 Download the Free Guided Notes Here: UnderstandTheMath.com/trigonometry

Explore Our Trigonometry and Precalculus Video Playlists

To further support your learning, check out these video playlists covering key trigonometry and precalculus topics:

📌 Full Trigonometry and Precalculus Video Series: Watch the Complete Playlist Here

📌 Trigonometry Example Problems Playlist: Watch the Example Problems Playlist Here

Prepare for Your Trigonometry and Precalculus Exams

If you're studying for an upcoming test or final exam, my Trigonometry and Precalculus Example Problems Playlist is designed to help you tackle challenging problems with confidence. Each video provides a step-by-step solution to key topics, including:

✔ Angles & Radians
✔ Right Triangle Trigonometry
✔ Trigonometric Functions & Graphs
✔ Trigonometric Identities & Equations
✔ Law of Sines & Law of Cosines
✔ Polar Coordinates & Applications
✔ Polynomial and Rational Functions
✔ Exponential and Logarithmic Functions
✔ And much more!

Why This Series is Different

My trigonometry and precalculus video series breaks down complex concepts into easy-to-follow lessons, making learning more accessible than traditional textbooks. Each topic is explained intuitively with visual aids, worked-out examples, and practical applications to help you gain a deeper understanding.

Who This Course is For:

✔ High school and college students taking trigonometry or precalculus
✔ Students preparing for exams or reviewing key concepts
✔ Anyone looking for a structured, step-by-step approach to learning trigonometry and precalculus
✔ Professionals applying trigonometry in physics, engineering, and other fields

Start Learning Today

If you're looking for an easy-to-follow, comprehensive resource to master trigonometry and precalculus, this video series with guided notes is your go-to learning tool. Whether you’re preparing for an exam or reinforcing key concepts, these resources will help you every step of the way.