Inverse Cosine and Tangent. Basic Trigonometric Equations for Cosine and Tangent

2021 ◽  
pp. 221-234
Keyword(s):  
Trigonometric Equations

Trigonometric equations

1983 ◽  
pp. 120-133
Author(s):  
B.D. Bunday ◽  
H. Mulholland
Keyword(s):  
Trigonometric Equations

scholarly journals 2D Graph Plotter and Visualizer

2021 ◽  
pp. 01-04
Author(s):  
Akash Lalitkumar Makwana ◽  
Atik Zakirhusen Mujawar ◽  
Lalit Shailesh Jain ◽  
Bhargavi Dalal ◽  
Smita Bansod
Keyword(s):  
Social Networks ◽  
Line Graph ◽  
Linear Equations ◽  
Science And Engineering ◽  
Graph Plotter ◽  
Trigonometric Equations ◽  
Pie Chart ◽  
New Algorithms

In many fields of science and engineering, we often encounter the problem of solving N linear equations of type x + y and trigonometric equations. All technological, biological and social networks can be represented as graphs. Therefore, graphs are used in the research of new algorithms and protocols based on simulation in various fields of science. We aim to create a python-based graph generator that will draw any type of equation i.e., linear, algebraic, trigonometric and logarithmic on the graph. More importantly, the application is designed to draw multiple graphs on the same canvas and then analyse the results. We have included one more module where user can upload a CSV file consisting of raw and get a desired pie chart, line graph as well as bar graph. Our system mainly focuses on generating a output for a later analysis by downloading the graphs they have plotted.

scholarly journals Student’s Difficulty Identification in Completing the Problem of Equation and Trigonometry Identities

2019 ◽  
Vol 2 (1) ◽  
pp. 34 ◽  
Author(s):  
Siti Maryam Rohimah ◽  
Sufyani Prabawanto
Keyword(s):  
High School Students ◽  
School Students ◽  
Quadratic Equations ◽  
Trigonometric Identity ◽  
Ability Tests ◽  
Solving Equations ◽  
Data Collection Technique ◽  
Trigonometric Equations ◽  
Identity Problems ◽  
Trigonometric Identities

This study aims to identify the types of difficulties experienced by high school students in solving equations and trigonometric identities. The method used in this research is descriptive qualitative research method because researchers want to describe or describe the facts of students' difficulties in solving equations and trigonometric identities. The data collection technique in this study is by using respondents' ability tests and interviews. Based on the results of data analysis, there are three aspects of students 'difficulties in solving trigonometric equations and also there are three aspects of students' difficulties in solving trigonometric identity problems. The difficulties of students in solving trigonometric equations, namely the difficulty of students in deciphering the form of the problem, difficulty in factoring in the form of trigonometric quadratic equations, and difficulties using the basic trigonometric equations. Whereas, the difficulties of students in solving trigonometric identity problems, namely the difficulty of students applying general trigonometry formulas, difficulty describing each of the trigonometric comparison relationships, and difficulties in performing algebraic calculations/computation.

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.

A SIMPLE METHOD TO DETERMINE THE DAYLIGHT FACTOR FROM THE VERTICAL DAYLIGHT FACTOR IN DIFFERENT STREET CANYON GEOMETRY

2016 ◽  
Vol 11 (2) ◽  
pp. 75-92
Author(s):  
Jorge S. Carlos
Keyword(s):  
Calculation Method ◽  
Street Canyon ◽  
Early Stage ◽  
Simple Calculation ◽  
Simple Method ◽  
Stage Design ◽  
Main Design ◽  
Early Stage Design ◽  
Trigonometric Equations ◽  
Graphical Presentation

This paper investigates the main characteristics of daylight on any window in a street canyon. The sky component and the light reflected from the surroundings are described to determine the vertical daylight factor (VDF). Several street canyon types are characterized taking into account their different height/width and any level of the window is analysed. A simple calculation method uses trigonometric equations based on the sky and the geometry of the canyon. The results were previously evaluated considering different daylight procedures obtained by other studies. This study reveals that the reflectance within an urban canyon plays an important role in the amount of daylight onto any window with more relevance in a deep canyon and low sky view. The graphical presentation that result from this investigation can rapidly assist building and urban designers in an early stage design where assumptions and the lay out of the main design take place.

Algorithm for rational determination of the area of a triangle for the development of students' creative thinking and practical application. Properties of the 90 Degrees angle tangent

2021 ◽  
pp. 46-55
Author(s):  
V. P. Zudin
Keyword(s):  
Creative Thinking ◽  
Visual Basic ◽  
Educational Process ◽  
Practical Application ◽  
Decimal System ◽  
Microsoft Word ◽  
Trigonometric Equations ◽  
Visual Basic For Application ◽  
Development Of Students

The article presents the formulas derived by the author for determining the area of a triangle by a side and two adjacent angles. These for - mulas are used to activate the educational process — students in practice figure out how to rationally determine the area of land plots, buildings, draw up and solve trigonometric equations, prove the properties of the tangent of an angle equal to 90 degrees, correct the graph of the function y = tg x. To carry out calculations of the areas of triangles, to prove the properties of 90 degree angle tangent, to solve trigonometric equations, programs are written in the Visual Basic For Application language in Microsoft Word. Using the binary-decimal system and VBA programs in Word, the value of the tangent of an angle is calculated so close to an angle of 90 degrees that this value can be roughly taken as the 90 degrees angle tangent. The study of this material at informatics lessons contributes to the development of creative thinking of students, increasing their motivation to study informatics and information technology.

Perturbational analysis of dual trigonometric series associated with boundary conditions of first and third kind

1978 ◽  
Vol 78 (3-4) ◽  
pp. 291-298 ◽  
Author(s):  
Robert B. Kelman
Keyword(s):  
Boundary Conditions ◽  
Trigonometric Series ◽  
Bounded Variation ◽  
Existence And Uniqueness ◽  
Potential Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Functions Of Bounded Variation ◽  
Uniqueness Theorems ◽  
Trigonometric Equations

SynopsisExistence and uniqueness theorems are established for dual trigonometric equations having right-hand sides that are given functions of bounded variation. The first equation in each pair has coefficients, say {Jn(n + h)} or (jn(n + h – ½)}, and the second equation coefficients {jn)}, where h is a nonnegative constant. A potential problem involving mixed boundary conditions of first and third kind is associated with each dual series. The potential problem is analysed using a stepwise perturbation procedure involving solutions in powers of h. The analysis demonstrates that the present dual series problem can be resolved if the dual series problem associated with the case h = 0 is solvable, the latter being a result obtained earlier.

A Novel Approach for Obtaining Assembly Modes of a 3UPS-S Fully Spherical Parallel Manipulator

2016 ◽  
Vol 32 (5) ◽  
pp. 555-563
Author(s):  
J. Enferadi
Keyword(s):  
Parallel Manipulator ◽  
Dynamics Simulation ◽  
Mathematical Tool ◽  
Forward Displacement ◽  
Rodrigues Formula ◽  
Coupled Equations ◽  
Novel Approach ◽  
Trigonometric Equations ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

AbstractThe 3(UPS)-S fully spherical parallel manipulator is the most famous fully spherical parallel manipulator (FSPM). In this paper, we propose a novel approach to model the forward displacement analysis of the manipulator to obtain its assembly modes. Rodrigues’ formula is used as a mathematical tool to perform the proposed modeling. Utilizing geometry of the manipulator, two coupled trigonometric equations are obtained. Using Bezout's elimination method, the two coupled equations are transformed to one polynomial of degree eight. Finally, an example is given with eight real solutions. Therefore, the degree of the polynomial is minimal and the introduced modeling method is optimal. This is very important to control modelling and dynamics simulation. Also, the proposed method can be extended to the other FSPMs (e.g., 3(RPSP)-S, 3(RPSP)-S and 3(RSS)-S).

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