Inverse trigonometric functions are an important topic in higher mathematics and mathematical analysis. They are used to determine angles from known trigonometric values and play a significant role in algebra, geometry, calculus, physics, and engineering. Understanding the properties of inverse trigonometric functions helps students solve complex equations, evaluate limits, compute derivatives and integrals, and analyze mathematical models. This article discusses the definitions, domains, ranges, fundamental properties, graphs, and derivatives of inverse trigonometric functions. Particular attention is given to their algebraic and analytical properties, which are essential in advanced mathematical studies.