Generalisasi Ketaksamaan Sinus pada Segitiga

Abstract

This study aims to find a generalization of the sine inequality of any triangles. This generalization is the general form of the sine inequality in a triangle when the angles given are not angles of the triangle, i.e. when the sum of the three angles is not equal to . The sine inequality that will be studied focuses on the inequalities of the sum and multiplication of sine in triangles. In the process, qualitative research methods are carried out in the form of literature review, namely studying the sum and the multiplication inequalities of sine in triangles which will then be developed and obtained new generalizations from the previous inequalities, namely generalizations of sine inequalities in triangles. These generalizations include generalizing the inequalities of the sum of sine in triangles and generalizing the inequalities of multiplication sine in triangles. To study this, it is necessary to first study the concepts of trigonometry, namely the definition of sine and cosine, the rules of sine and cosine; the relationship of the sine cosine to the sides of the triangle; the relationship of the radius of the circumcircle of the triangle to the sides and angles of the triangle; and arithmetic and geometric mean inequalities.The results of this study obtained the generalization of the sine inequality of any triangles.

Keywords: inequality, sine, triangle