Revisiting a Proof of the Sine Theorem

Abstract

The author of the article outlines, that in school geometry course, the sine theorem and the cosine theorem are well known. In this course, they are proved by the authors of the textbook in a way different from the one that is presented in the article. The article considers the author's method of proving the sine theorem unknown in the literature sources and based on the vector-coordinate method; two more theorems are also proved, one of which concerns the calculation of the inscribed angle in the circle, and the other concerns the calculation of viewing angles of the chord of the circle; one task is proposed by the author for independent work, in which the object of research is the chord of a circle. Research results. A proof of the sine theorem, presented by the author on the basis of his technique, undoubtedly quicken public interest. The material can serve as a basis for organizing educational and research activities of students in mathematics. It is concluded that educational and research activities of students in mathematics can be effectively organized when: establishing the essential properties of concepts; identifying the relationship of this concept with other concepts; searching for other methods of proving theorems; formulating the inverse theorem and establishing its truth; classification of mathematical objects and relations between them; solving mathematical problems in various ways and methods; drawing up new tasks that result from already solved ones; providing examples and counterexamples that illustrate a particular fact, etc.

Keywords

• chord of circle
• cosine theorem
• inscribed angle in a circle
• scalar vector product
• sine theorem
• vector-coordinate method