title: ÐÐ»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸ ÑÑÐµÐ±Ð½ÑÑ Ð·Ð°Ð´Ð°Ñ Ð¿Ð¾ ÑÑÐ¸Ð³Ð¾Ð½Ð¾Ð¼ÐµÑÑÐ¸Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Algorithm for automatic generation of trigonometric training tasks
Creators: name: ÐÑÐ¸ÑÐ°ÐµÐ½ÐºÐ¾, ÐÐ¸ÐºÐ¸ÑÐ°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð¢ÑÐ¸Ð³Ð¾Ð½Ð¾Ð¼ÐµÑÑÐ¸Ñ
ÐÐ»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ
Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð°ÑÐ¸Ñ
Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¸Ð¼Ð²Ð¾Ð»ÑÐ½ÑÑ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ð¹
automation
symbolic expressions transformations

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÐ»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸ ÑÑÐµÐ±Ð½ÑÑ Ð·Ð°Ð´Ð°Ñ Ð¿Ð¾ ÑÑÐ¸Ð³Ð¾Ð½Ð¾Ð¼ÐµÑÑÐ¸Ð¸Â». ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¿ÑÐ¾ÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¸ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸ ÑÑÐ¸Ð³Ð¾Ð½Ð¾Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð·Ð°Ð´Ð°Ñ Ð½Ð° Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ð¹. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð´ÑÐ¾Ð±Ð½Ð¾ ÑÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ñ ÑÑÐµÐ±Ð¾Ð²Ð°Ð½Ð¸Ñ Ð´Ð»Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸ Ð·Ð°Ð´Ð°Ñ â Ð±ÑÐ»Ð¸ Ð¾Ð¿Ð¸ÑÐ°Ð½Ñ Ð²ÑÐ¾Ð´Ð½ÑÐµ Ð½Ð°ÑÑÑÐ¾Ð¹ÐºÐ¸ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸, Ð° ÑÐ°ÐºÐ¶Ðµ ÐºÑÐ¸ÑÐµÑÐ¸Ð¸ ÐºÐ°ÑÐµÑÑÐ²Ð° ÑÑÐµÐ±Ð½ÑÑ Ð·Ð°Ð´Ð°Ñ. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ» Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½ Ð¼ÐµÑÐ¾Ð´ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸ Ð·Ð°Ð´Ð°Ñ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð·Ð°Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ ÑÑÐ°ÑÑÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ¸Ð¼Ð²Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ñ. ÐÐ»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸ ÑÑÐ¸Ð³Ð¾Ð½Ð¾Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð·Ð°Ð´Ð°Ñ Ð±ÑÐ» ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½ Ð½Ð° Ð±Ð°Ð·Ðµ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ TWF Ð¸ Ð´Ð¾Ð²ÐµÐ´ÑÐ½ Ð´Ð¾ ÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÐµÐ»Ñ. Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸ Ð±ÑÐ»Ð° Ð¿ÑÐ¾ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð° Ð¿Ð¾ ÑÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÐ¼ ÐºÑÐ¸ÑÐµÑÐ¸ÑÐ¼ ÐºÐ°ÑÐµÑÑÐ²Ð° Ð¸ ÑÐ¾Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð° Ñ Ð¿ÐµÑÐ²Ð¾Ð¹ Ð²ÐµÑÑÐ¸ÐµÐ¹ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð°, ÑÑÑÐµÑÑÐ²Ð¾Ð²Ð°Ð²ÑÐµÐ¹ Ð² Ð¿ÑÐ¾ÐµÐºÑÐµ TWF Ð½Ð° Ð¼Ð¾Ð¼ÐµÐ½Ñ Ð½Ð°ÑÐ°Ð»Ð° ÑÐ°Ð±Ð¾ÑÑ. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ» ÑÐ´ÐµÐ»Ð°Ð½ Ð²ÑÐ²Ð¾Ð´, ÑÑÐ¾ ÑÐ´Ð°Ð»Ð¾ÑÑ Ð´Ð¾ÑÑÐ¸Ð³Ð½ÑÑÑ Ð·Ð½Ð°ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ ÑÐ»ÑÑÑÐµÐ½Ð¸Ñ ÐºÐ°ÑÐµÑÑÐ²Ð° Ð³ÐµÐ½ÐµÑÐ¸ÑÑÐµÐ¼ÑÑ Ð·Ð°Ð´Ð°Ñ. Ð¡ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° ÑÑÐ¸ÑÐµÐ»Ñ ÑÐ¼Ð¾Ð³ÑÑ Ð³ÐµÐ½ÐµÑÐ¸ÑÐ¾Ð²Ð°ÑÑ Ð·Ð°Ð´Ð°ÑÐ¸ Ð´Ð»Ñ ÑÐ°Ð¼Ð¾ÑÑÐ¾ÑÑÐµÐ»ÑÐ½ÑÑ Ð¸ ÐºÐ¾Ð½ÑÑÐ¾Ð»ÑÐ½ÑÑ ÑÐ°Ð±Ð¾Ñ, Ð° ÑÑÐ°ÑÐ¸ÐµÑÑ â ÑÑÐµÐ½Ð¸ÑÐ¾Ð²Ð°ÑÑ Ð½Ð°Ð²ÑÐºÐ¸ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð·Ð°Ð´Ð°Ñ Ð½Ð° Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¾ÑÐ¼ÑÐ». Ð¢Ð°ÐºÐ¶Ðµ Ð´Ð°Ð½Ð½ÑÐ¹ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½ Ð² ÑÐ¸ÑÑÐµÐ¼Ñ Ð¸Ð³ÑÐ¾ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÑÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¾ÐµÐºÑÐ° MathHelper.
description: Topic of the graduate qualification work is "Algorithm for automatic generation of trigonometric training tasks". The given work is devoted to the design and implementation of an algorithm for the automatic generation of trigonometric expression transformation tasks.In the given work, the requirements for the task generation algorithm were formulated in details: the input generation settings were described, as well as the criteria for the quality of training tasks. A method for generating tasks based on transformations of a given initial symbolic expression was proposed. The algorithm for generating trigonometric tasks was implemented on the basis of the TWF library and delivered to the end user. The implementation of the algorithm was tested according to the formulated quality criteria and compared with the first version of the algorithm existed in TWF project at the time the work started. As a result, it was concluded that significant improvement in the quality of generated tasks has been achieved.With the help of the implemented algorithm, teachers will be able to generate tasks for verification works and tests, and students will be able to train the skills of solving transforming formulas tasks. Also, this algorithm can be integrated into the gamification systems of the MathHelper research project.