Una nueva prueba para una conjetura de Özban

2021 ◽  
Vol 39 (2) ◽  
Author(s):  
Aníbal Coronel ◽  
Esperanza Lozada
Keyword(s):  
Trigonometric Inequalities

En este artículo presentamos una prueba corta y elemental de la siguiente desigualdad algebraico-trigonométrica de tipo Laub-Ilani: cos(xy) + cos(yx) ≥ cos(xx) + cos(yy) para x, y ∈ [0, π/2] que fue conjeturada por Özban [‘New algebraic-trigonometric inequalities of Laub-Ilani type’, Bull. Aust. Math. Soc. 96 (2017), 87–97] y recientemente probada por Matejíčka [‘Proof of one open inequality of Laub-Ilani type’, Journal of Mathematical Inequalities, 14 (2020), 83–98]. La prueba se basa en las propiedades de las funciones potenciales-exponenciales y trigonométricas.

scholarly journals ABOUT DEVELOPMENT OF STUDENTS ' THINKING WHEN SOLVING TRIGONOMETRIC EQUATIONS AND INEQUALITIES IN THE SCHOOL ALGEBRA COURSE

2020 ◽  
Vol 69 (1) ◽  
pp. 138-143
Author(s):  
D.M. Nurbayeva ◽  
◽  
Zh.M. Nurmukhamedova ◽  
S. Yeraliyev ◽  
B.M. Kossanov ◽  
...  
Keyword(s):  
Unit Circle ◽  
Circle Method ◽  
Trigonometric Functions ◽  
Detailed Explanation ◽  
Trigonometric Inequalities ◽  
Trigonometric Equations ◽  
Development Of Students

The article deals with solutions of trigonometric inequalities using the unit circle. Specific examples show its application for all trigonometric functions, namely sinus, cosine, tangent and cotangent. An explanation of how to correctly define the period for solving inequalities is also provided. Before analyzing the solution to trigonometric inequalities, the authors present the solution of trigonometric equations according to the formula, but his roots are depicted on the unit circle, where detailed explanation of the record of solutions of this equation. The pictures in the article demonstrate the images that should be presented by the teacher on the blackboard when solving trigonometric inequalities. The article is written in an accessible language, when reading which the unit circle method will be understandable not only to current teachers, but also to students of Junior courses of pedagogical universities.

scholarly journals Simple efficient bounds for arcsine and arctangent functions

2021 ◽  
Author(s):  
Yogesh J. Bagul ◽  
Ramkrishna M. Dhaigude
Keyword(s):  
Computationally Efficient ◽  
Sharp Bounds ◽  
Trigonometric Inequalities

Abstract The aim of this paper is to present new, simple and sufficiently sharp bounds for arcsine and arctangent functions. Some of the bounds are computationally efficient while others are efficient to approximate the integrals Int_{a}^{b} (arcsin x)/x dx and Int_{a}^{b} (arctan x)/x dx. As a matter of interest, several other sharp and generalized inequalities for (arcsin x)/x and (arctan x)/x are also established which are efficient to give some known and other trigonometric inequalities

scholarly journals Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Branko Malešević ◽  
Tatjana Lutovac ◽  
Marija Rašajski ◽  
Cristinel Mortici
Keyword(s):  
Natural Approach ◽  
Trigonometric Inequalities

Exploring Geometric Maxima and Minima

1969 ◽  
Vol 62 (2) ◽  
pp. 85-90
Author(s):  
J. Garfunkel
Keyword(s):  
Mathematics Teacher ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Trigonometric Inequalities

In an Article that appeared in The Mathematics Teacher, * many interesting geometric as well as trigonometric inequalities were developed by starting with the theorem that the arithmetic mean of n positive quantities is not less than their geometric mean. The author also developed a few geometric maxima and minima properties in this manner.

A sequence of sharp trigonometric inequalities

2015 ◽  
Vol 141 (1) ◽  
pp. 61-64
Author(s):  
J. B. M. Melissen ◽  
M. El Ghami
Keyword(s):  
Trigonometric Inequalities
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