Foundations of Trigonometry: Functions, Equations, and Inequalities

Trigonometry is a vital pillar of mathematics, yet many struggle with visualizing the unit circle or solving complex equations. Understanding these concepts is essential for success in calculus, physics, and engineering. This text-based course guides you from the absolute basics of angles and triangles to confidently solving trigonometric equations and inequalities. What you'll learn: Understand fundamental trigonometric ratios, functions, and the properties of the unit circle; Memorize and apply key trigonometric table values and basic identities; Solve linear and quadratic trigonometric equations systematically; Analyze and solve trigonometric inequalities using algebraic and interval notation; Graph trigonometric functions and identify their domain, range, amplitude, and period; Apply modern mathematical modeling concepts to real-world periodic phenomena. You will start with essential terminology, basic definitions, and the unit circle before progressing to algebraic techniques for solving equations and graphing functions. This course is designed for absolute beginners, high school students, or anyone looking to refresh their mathematical foundations with no prior trigonometry experience required. Start reading today to build a strong, confident foundation in trigonometry.