Foundational Trigonometry: Angles, Ratios, and Functions

Many foundational STEM subjects rely on a deep understanding of trigonometry, but the initial concepts can often feel abstract. This course breaks down the fundamentals systematically through clear, written explanations and focused practice. By the end of this course, you will have a robust conceptual framework for working with angles, defining trigonometric functions, proving identities, and applying these principles to solve geometric and real-world problems. What you'll learn: Understand the definitions of angles in standard position, including radian and degree measure, and the concept of the unit circle. Master the six fundamental trigonometric ratios and their reciprocal relationships within right triangles. Apply key trigonometric identities, including Pythagorean, sum/difference, and double-angle formulas, to simplify expressions and prove relationships. Analyze and graph the properties of the sine, cosine, and tangent functions, including amplitude, period, and phase shift. Practice solving right-triangle problems and basic applications involving bearing and elevation. The course begins with foundational definitions and angular measurement systems before introducing the unit circle and the six primary functions. We then move into mastering key identities and concluding with practical problem-solving techniques. This course is designed exclusively for beginners who need a strong, academic foundation in trigonometry before progressing to pre-calculus, physics, or engineering studies. No prior mathematical knowledge beyond basic algebra is required. Start building your mathematical foundation today through focused, written instruction and practice.