Overview
What is trigonometry and triangles, How angles work—degree and radian measure, angular velocity, and reference angles, The Pythagorean Theorem, distance formula, and how to determine right triangles, Definitions and properties of the six trigonometric ratios, including reciprocal and quotient identities, How to solve right triangles, including real-world applications like measuring heights and distances, The unit circle, trigonometric identities, and graphing sine, cosine, tangent, and their transformations, How to use double angle, half angle, and sum-to-product identities to simplify expressions and solve equations, Techniques for solving trigonometric equations, including those with modified periods and identities, The Law of Sines, Law of Cosines, and how to solve oblique triangles, including the ambiguous case, How to compute area of triangles using trigonometric formulas, including Heron’s formula, Introduction to vectors, including static equilibrium, dot product, and angle between vectors, Deep dive into complex numbers, including polar form, Euler’s identity, and De Moivre’s Theorem, How to work with parametric equations, polar coordinates, and graph polar functions
High school and college students studying geometry, trigonometry, or precalculus, STEM learners in physics, engineering, or computer science, Educators seeking a structured and visual approach to teaching trigonometry, Anyone who wants to understand the math behind motion, waves, and circular systems
Basic understanding of algebra and geometry, A willingness to engage with visual and analytical problem-solving
Mastering Trigonometry: From Triangles to Polar Graphs and Complex Numbers
Trigonometry is often introduced as a tool for solving triangles—but in reality, it’s a gateway to understanding the geometry of motion, waves, rotations, and even complex numbers. This course is designed to redefine how you learn trigonometry, offering a comprehensive, structured, and visually intuitive approach that goes far beyond textbook basics.
You’ll begin with the essentials—right triangles, the Pythagorean Theorem, and angle relationships—and quickly progress to unit circle trigonometry, graphing sinusoidal functions, and solving real-world problems involving elevation, distance, and circular motion. From there, you’ll explore trigonometric identities, inverse functions, and equation solving techniques that are foundational for calculus and physics.
But what truly sets this course apart is its breadth and depth. You’ll go beyond triangles to study vectors, complex numbers, parametric equations, and polar coordinates—topics that are rarely covered in standard trigonometry courses but are essential for advanced STEM fields. You’ll learn how trigonometry powers engineering, navigation, signal processing, and computer graphics, and how it connects algebra, geometry, and analysis into a unified mathematical language.
Why Take This Course?
To gain a deep, intuitive understanding of trigonometry—not just memorize formulas
To prepare for calculus, physics, engineering, or any STEM discipline that relies on trigonometric reasoning
To learn real-world applications of trigonometry in motion, measurement, and modeling
To explore advanced topics like complex numbers, polar graphs, and parametric equations in a clear and accessible way
To build confidence in problem-solving, graph interpretation, and mathematical thinking
What Makes This Course Unique
Comprehensive Coverage: From basic triangles to advanced polar graphs and complex roots
Visual Learning: Diagrams, animations, and graphing techniques that make abstract ideas concrete
Real-World Applications: Physics, engineering, navigation, and more
Step-by-Step Instruction: Clear explanations, guided examples, and problem-solving strategies
Advanced Topics Included: Vectors, Euler’s identity, De Moivre’s Theorem, and parametric curves
Designed for All Levels: Whether you're reviewing or learning for the first time, this course adapts to your pace
Science Academy
The Science and Math Academy makes complex concepts simple, engaging, and practical for learners of all levels. Covering a wide range of topics—from fundamental mathematics and physics to advanced problem-solving and applied sciences—the academy helps students build a strong foundation while also developing critical thinking and analytical skills. With clear explanations, real-world examples, and interactive lessons, it serves as a comprehensive learning hub for school students, university learners, and professionals seeking to refresh or strengthen their knowledge in science and mathematics.