正弦函数和余弦函数的Milosevic型不等式的加强形式  

Sharpening Versions of Milosevic-type Inequalities Associated with Sine Function and Cosine Function

作　　者：赖村如 吴善和 LAI Cunru;WU Shanhe(Longyan No.7 Middle School;Longyan University,Longyan,Fujian 364000,China)

机构地区：[1]龙岩市第七中学 [2]龙岩学院师范教育学院,福建龙岩364000

出　　处：《龙岩学院学报》2022年第5期110-117,共8页Journal of Longyan University

基　　金：福建省本科高校教育教学改革研究项目(FBJG20210184);龙岩学院首批面向龙岩市基础教育教学改革研究项目(2020JCJY020)。

摘　　要：正弦函数和余弦函数的Milosevic型不等式刻画了三角形的三边长和三内角及其外接圆半径和内切圆半径之间的关系,有着丰富的内涵。作者构造关于外接圆半径和内切圆半径的多项式函数,利用其给出正弦函数和余弦函数的Milosevic型不等式的更精确的上界和下界,所得结果统一加强了以往文献中相关的Milosevic型不等式。The Milosevic-type inequalities associated with the sine function and cosine function contain abundant connotations,which depict a correlation between three angles,corresponding sides,circumradius and inradius of a triangle.In this paper,the authors construct the polynomial function which depends on the circumradius and inradius of a triangle and use the results to establish more accurate lower bound and upper bound of Milosevic-type inequalities for sine function and cosine function.The results obtained provide a unified sharpening of some Milosevic-type inequalities presented in earlier papers.

关 键 词：Milosevic型不等式 EULER不等式 加强形式 正弦函数 余弦函数 

分 类 号：O122.3[理学—数学]