Abstract
The process of teaching mathematics is carried out through problem-solving, among which research-oriented problems are of great importance. Inequalities involving inverse trigonometric functions can be classified as such complex and interesting tasks. For high school students, problems related to inverse trigonometric functions often cause difficulties. As practice shows, while students can successfully complete tasks to calculate the values of inverse trigonometric functions, many encounter difficulties when dealing with inequalities that contain these exact functions. The main reason for this is the insufficient time allocated to teaching inverse trigonometric functions in the school curriculum. From a logical standpoint, just as logarithms are essential for exponential functions, inverse trigonometric functions are an equally necessary concept for trigonometric functions. Problems on this topic not only complement trigonometry but also significantly contribute to developing the flexibility of students' mathematical thinking. Working with inverse trigonometric functions allows students to go "beyond the textbook," initiate creative research work, and enhance their cognitive abilities. Although problems related to inverse trigonometric functions are included in the school curriculum, educational and methodological materials do not pay adequate attention to this topic. Many textbooks fail to fully explain the methodology for solving even simple equations and inequalities. As a result, students' learning outcomes on this topic indicate low performance levels. However, solving inequalities with inverse trigonometric functions is a crucial tool that helps systematize the knowledge students have acquired throughout the entire trigonometry course, assess their depth of understanding, and master the core concepts of the section. In order to fill these gaps, this article examines effective methods for solving inverse trigonometric inequalities.