Abstract
This article discusses the problem of developing methodological foundations for teaching high school students to solve transcendental equations and inequalities, as well as their systems. The main purpose of the study is to combine students' theoretical knowledge on this topic with practical knowledge, to develop effective teaching methods that enhance their logical thinking, analytical, and quantitative analytical abilities, and to introduce them into the educational process. The article analyzes the main types and properties of transcendental equations, suggests traditional and new methods for solving them. The teaching methodology consists of four stages: the assimilation of theoretical material, the performance of practical tasks, the use of information technology, creative tasks and teamwork. Each stage aims to consolidate students' theoretical knowledge and develop problem-solving skills through various methods. During the study, a specially developed teaching methodology was used for the students in the experimental group. The results of the experiment showed that the students' ability to solve transcendental equations and inequalities has improved significantly. The average student score increased from 44 to 76 on the final test, demonstrating the effectiveness of the new methodology. In addition, student attendance, interest in the subject, and creative abilities have increased. The methodology presented in the article enables students to improve their mathematical literacy, become more interested in the subject, and enhance the effectiveness of the educational process. The results of this study will serve as a basis for developing proposals to improve the teaching methods of transcendental equations and inequalities in the education system of Kazakhstan.