scholarly journals ESSENTIAL TRIGONOMTERY WITHOUT GEOMETRY PART II: GENERALIZATIONS AND APPLICATIONS

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
John Gresham ◽  
Bryant Wyatt ◽  
Jesse Crawford
Keyword(s):  
Analytical Methods ◽  
Geometric Constructions ◽  
Conservation Of Energy ◽  
The Law ◽  
Sine And Cosine Functions ◽  
Cosine Functions

Abstract In a previous paper (Gresham et al. 2019), the properties, theorems, and identities of the sine and cosine functions were developed using only analytical methods and without geometric constructions. We follow those results and use them to develop generalizations of the key theorems of trigonometry, again using purely analytical methods. We conclude with a connection to the Law of Conservation of Energy in physics.

scholarly journals ESSENTIAL TRIGONOMETRY WITHOUT GEOMETRY

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
John Gresham ◽  
Bryant Wyatt ◽  
Jesse Crawford
Keyword(s):  
Unit Circle ◽  
Elementary Level ◽  
Comprehensive Treatment ◽  
Advanced Mathematics ◽  
Trigonometric Functions ◽  
Geometric Constructions ◽  
Rigorous Approach ◽  
Sine And Cosine Functions ◽  
Cosine Functions

Abstract The development of the trigonometric functions in introductory texts usually follows geometric constructions using right triangles or the unit circle. While these methods are satisfactory at the elementary level, advanced mathematics demands a more rigorous approach. Our purpose here is to revisit elementary trigonometry from an entirely analytic perspective. We will give a comprehensive treatment of the sine and cosine functions and will show how to derive the familiar theorems of trigonometry without reference to geometric definitions or constructions. Supplemental material is available for this article online.

Some Mellin-type Definite Integrals Involving Sine and Cosine Functions

2019 ◽  
Vol 10 (1) ◽  
pp. 222-237
Author(s):  
M. I. Qureshi ◽  
Kaleem A. Quraishi ◽  
Dilshad Ahamad
Keyword(s):  
Definite Integrals ◽  
Sine And Cosine Functions ◽  
Cosine Functions

Technical condition of agricultural machinery

2021 ◽  
pp. 53-61
Author(s):  
A. A. Solomashkin ◽  
M. N. Kostomakhin
Keyword(s):  
Energy Balance ◽  
Object Oriented ◽  
Technical Condition ◽  
Object Oriented Programming ◽  
Agricultural Machinery ◽  
Working Capacity ◽  
Conservation Of Energy ◽  
Basic Functions ◽  
The Law ◽  
Expanded Concept

Two basic functions of the machine, consumer and technical are given. Application the law of conservation of energy is shown in case of the description of an energy balance of an element of the machine. The expanded concept of technical condition in relation to the machine is this, parameters of technical condition are justified. Communications of technical condition with operability and working capacity and also communication of operability of an element of the machine with its efficiency are defined. The possibility of representation of technical condition in the form of сlass in object-oriented programming is revealed.

SINS Installation Error Calibration Based on Multi-Position Combinations

2011 ◽  
Vol 383-390 ◽  
pp. 4213-4220
Author(s):  
Zhen Huan Wang ◽  
Xi Jun Chen ◽  
Qing Shuang Zeng
Keyword(s):  
Theoretical Analysis ◽  
Least Squares ◽  
Rotation Rate ◽  
Scale Factor ◽  
New Method ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Error Calibration ◽  
Sine And Cosine Functions ◽  
Cosine Functions

A new method is proposed to calibrate the installation errors of SINS. According to the method, the installation errors of the gyro and accelerometer can be calibrated simultaneously, which not depend on latitude, gravity, scale factor and earth's rotation rate. By the multi-position combinations, the installation errors of the gyro and accelerometer are modulated into the sine and cosine functions, which can be identified respectively based on the least squares. In order to verify the correctness of the theoretical analysis, the SINS is experimented by a three-axis turntable, and the installation errors of the gyro and accelerometer are identified respectively according to the proposed method. After the compensation of the installation error, the accuracy of the SINS is improved significantly.

2. Planet Earth

2018 ◽  
pp. 6-21
Author(s):  
William Lowrie
Keyword(s):  
Big Bang ◽  
Chandler Wobble ◽  
Planetary Motion ◽  
Milankovitch Cycles ◽  
The Sun ◽  
Conservation Of Energy ◽  
The Earth ◽  
The Law ◽  
Physical Laws ◽  
The Big Bang

Two important physical laws determine the behaviour of the Earth as a planet and the relationship between the Sun and its planets: the law of conservation of energy and the law of conservation of angular momentum. ‘Planet Earth’ explains these laws along with the ‘Big Bang’ theory that describes the formation of the solar system: the Sun; the eight planets divided into the inner, terrestrial planets (Mercury, Venus, the Earth, and Mars) and the outer, giant planets (Jupiter, Saturn, Uranus, and Neptune); and the Trans-Neptunian objects that lie beyond Neptune. Kepler’s laws of planetary motion, the Chandler wobble, the effects of the Moon and Jupiter on the Earth’s rotation, and the Milankovitch cycles of climatic variation are also discussed.

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