Optimal ways of teaching the topic «trigonometric equations» in the school mathematics course

The article selected for research is dedicated to the optimal methods of teaching trigonometric equations in the high school mathematics course based on the curriculum. In the article, it is also confirmed that the studied material is the logical conclusion of the trigonometry course, the final result of the passed theoretical knowledge. The topic of trigonometric equations and inequalities provides excellent examples and problems of integration between algebra, geometry and other disciplines. Trigonometry is closely related to both geometry and algebra in its characteristics, and this connection is reflected in the content of the school mathematics course. Thus, trigonometry is used in geometry in metric relationships in right triangles, in the definition of the sine, cosine, tangent and cotangent of an acute angle, in the theorem of sines and cosines, in the relationship formulas between sides and radii when circles are drawn inside and outside regular polygons, in area formulas of many geometric figures, etc., in algebra and in the course, the main formulas of trigonometry, trigonometric equations and inequalities, etc. are given in the sections. Our main goal in the dissertation is to explain the place and importance of trigonometric equations and inequalities in the school mathematics course, to show the role of trigonometric equations in the equation family, and to determine the methodical features of its solution. At the same time, in the process of teaching trigonometric equations and inequalities, the solution of algebraic equations included in the family of equations is also considered, and this requires both the teacher and the student to teach and learn the high school mathematics course in a complete, integral way