One of the methods of root selection in solving trigonometric equations

Abstract

When preparing students in grades 10-11 for the profile USE in mathematics, there are difficulties in selecting the roots of the trigonometric equation that belong to a given interval. There are several methods of root selection, but there is no perfect one – each of these methods has its own weaknesses. We want to propose a method that, in our opinion, allows students to more successfully select the roots in trigonometric equations. In a school mathematics course, the most common way to select roots is to use a trigonometric circle or to select roots using a double inequality that defines a given interval. The situation in real tasks is complicated by the fact that the specified range for the values of the roots goes beyond one circle. This fact complicates the selection of roots on the circle itself, since it requires students to have a more complex orientation on it. If the root value cannot be explicitly written in the radian measure, then selecting the roots using the double inequality becomes problematic. The basic level math exam paper consists of one part, including 20 tasks with a short answer. All tasks are aimed at testing the development of basic skills and practical skills of applying mathematical knowledge in everyday situations. The answer to each of the tasks 1-20 is an integer, a finite decimal, or a sequence of digits.