Tracy Gitonga
Modeling Data With Trigonometric Functions
Precalculus 1113-213
October 18, 2011

Real-life math is used in many activities that people do in a daily basis. In the next few paragraphs I will be explaining how to use a real world data and model it with a sine function of the form of y= a sin K (x-b). The graphs will use the law of sine which is defines as, “a law stating that the ratio of the sine of an arc of a spherical triangle to the sine of the opposite angle is the same for all three arcs.” The following table gives the number of hours of daylight in Philadelphia, Pennsylvania.

Day | | Mar 21 | Apr 21 | May 21 | | June 21 | | July 21 | | Aug 21 | | Sept 21 | | Oct 21 | | Nov 21 | | Dec 21 | Hours of Day-light | | 12 | 13.7 | 14.2 | | 14.8 | | 14.2 | | 13.7 | | 12 | | 11.4| | 9.8 | | 9.2 |

While plotting the data, I realized that the sine function works better because the graph begins from the point (0) on the x-axis of the graph. Firstly, I realized I need to be able to find my equation before formulating a graph. My equation is y= a sin K (x-b). I need to find the “a”, which stands for amplitude, “the maximum extent of a vibration or oscillation, measured from the position of equilibrium.” I took the difference between the highest and lowest daylight hours reading in the table and divided by two.

14.8 – 9.2 = 5.6/2
A= 2.8
Secondly, I figured the period which is defined as, “a space of time between two events or a portion of time.” The formula is 2 /K
2 /k = 365
k = 2 /365
P= 2 /365
Thirdly, the phase shift “represents the amount a wave has shifted horizontally from the original wave.” I was able to figure the phase shift by the information given which stated that, “the time to be in days. March 21 is the 80th day of the year.” With that given I just took the number before what was given equaling it to 79. Our phase shift stands for b in our formula.

...The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) include the domain, range, period, asymptotes and amplitudes.
The domain of a cosine and sine function is all real numbers and the range is -1 to 1. The period is 2π, and the amplitude is 1. They have no asymptotes. The domain of tangent is all real numbers except for π2+kπ. The range is all real numbers and the period is π. Tan has no amplitude and has asymptotes when x= π2+kπ.
The domain of a secant function is all real numbers except for π2+kπ. The domain of a cosecant function is all real numbers except for kπ. The range of both is (-∞.-1]U[1,∞) and the period is 2π. Secant has asymptotes when x=π2+kπ. Cosecant has asymptotes when x=kπ. They have no amplitude. Cotangent’s domain is all real numbers except for kπ. The range is all real numbers and the period is π. It has no amplitude and has asymptotes when x=kπ.
In an inverse function, the x coordinate, or the domain, and the y coordinate, the range, switch places. Since only one to one functions have inverses, we take the interval -π2 to π2, which contains all the possible values of the sine function. Now, the new domain is [-π2, π2], while the range stays the same. We then switch the domain and the range, so the domain and range of arcsin (x) is [-1,1] and [-π2, π2]. For cosine, the interval [0,π] contains all...

...Lab – Data Analysis and DataModeling in Visio
Overview
In this lab, we will learn to draw with Microsoft Visio the ERD’s we created in class.
Learning Objectives
Upon completion of this learning unit you should be able to:
▪ Understand the concept of datamodeling
▪ Develop business rules
▪ Develop and apply good data naming conventions
▪ Construct simpledata models using Entity Relationship Diagrams (ERDs)
▪ Develop entity relationships and define various types of attributes
Lab Goals
Our lab goals are to:
1. Learn to build conceptual models in Microsoft Visio.
2. Create the 5 ERDs from class in Microsoft Visio.
You will accomplish this by drawing the 4 diagrams from the class exercise. You will have to hand in all 4 diagrams by FTPing them to your account space on the IST-S-STUDENTS server and then pasting the url to the diagram in the text boxes for this week’s learning unit assessment.
What you will need to begin
1. A copy of Microsoft Visio 2003 (or higher)
2. The Visio Conceptual Modeling Stencil conceptual modeling.vss (should be with the other files from this week’s lesson)
3. The class exercises from this week (should also be with the other files from week’s lesson.)
Part 1: Getting Ready for Using Microsoft Visio for Conceptual Modeling...

...Chapter 2: Linear Functions
Chapter one was a window that gave us a peek into the entire course. Our goal was to understand the basic structure of functions and function notation, the toolkit functions, domain and range, how to recognize and understand composition and transformations of functions and how to understand and utilize inverse functions. With these basic components in hand we will further research the specific details and intricacies of each type of function in our toolkit and use them to model the world around us.
Mathematical Modeling
As we approach day to day life we often need to quantify the things around us, giving structure and numeric value to various situations. This ability to add structure enables us to make choices based on patterns we see that are weighted and systematic. With this structure in place we can model and even predict behavior to make decisions. Adding a numerical structure to a real world situation is called Mathematical Modeling.
When modeling real world scenarios, there are some common growth patterns that are regularly observed. We will devote this chapter and the rest of the book to the study of the functions used to model these growth patterns.
Section 2.1 Linear Functions 99
Section 2.2 Graphs of Linear Functions 111...

...System Concepts for DataModeling
Crystal M. Reedus
CIS 210
November 21, 2010
Abstract
Datamodeling techniques and methodologies are used to model data in a standard, consistent, predictable manner in order to manage it as a resource. Data models support data and computer systems by providing the definition and format of data. From a modeling perspective, the entire problem domain is viewed as a collection of class hierarchies (of objects) that are connected by messages.
Datamodeling techniques and methodologies are used to model data in a standard, consistent, predictable manner in order to manage it as a resource. Datamodeling may be performed during various types of projects and in multiple phases of projects. Data models are progressive; there is no such thing as the final data model for a business or application. Instead a data model should be considered a living document that will change in response to a changing business.
In this paper the focus will be on next generation systems, objected oriented systems and reversed engineered data models. The concept of a data model is really the design for that specific use. Since not every system uses data models the same then there is...

...DataModeling Concepts
COM 660
DataModeling Concepts
Following document explains what are data models and the importance of data model. Building a good data model helps organizations in software development, data base design and product maintenance. The document explains the theory, even if it looks like the organizations are spending substantial amount of resources on developing data models, but still it helps organization, keeping the costs low and build a better product.
Database constitutes of data structures and is represented by conceptual data structures. Data models are abstract models which is required to define how data can be consumed and put to effective use. The main reason why construction of data model is required because, data model helps systems to manage large amounts of both structured and unstructured data. In the software development process the projects focus mainly on the design of conceptual data model, or a logical data model. After the concept is defined and approved, physical data model will be created. Logical and physical models exhibit the two different ways of explaining the data models. The logical description explains core design of the model, which is not...

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Modeling Aspects By Satish K Yellanki
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Business Process...

...Vilnius Gediminas Technical University
Jelena Mamčenko
Lecture Notes
on
INFORMATION RESOURCES
Part I
Introduction to Dta Modeling and MSAccess
Code FMITB02004
Course title Information Resourses
Course volume 3,0 cr. (4,50 ECTS cr.)
Teaching methods (Full-time, daytime studies):
Lectures - 16 h per semestre
Laboratory works - 32 h per semestre
Individual work - 72 h per semester
Course aim
Understandig of models and system of information resourses.
Jelena Mamčenko
Introduction to DataModeling and MSAccess
CONTENT
1
2
3
4
5
6
Introduction to DataModeling ............................................................................................................... 5
1.1
DataModeling Overview ............................................................................................................... 5
1.1.1
Methodology .......................................................................................................................... 6
1.1.2
DataModeling In the Context of Database Design................................................................ 6
1.1.3
Components of A Data Model................................................................................................ 6
1.1.4
Why is DataModeling Important?...

...Lecture Notes 1
DataModeling
ADBMS Lecture Notes 1: Prepared by Engr. Cherryl D. Cordova, MSIT
1
• Database: A collection of related data. • Data: Known facts that can be recorded and have an implicit meaning.
– An integrated collection of more-or-less permanent data.
• Mini-world: Some part of the real world about which data is stored in a database. For example, student grades and transcripts at a university. • Database Management System (DBMS): A software package/ system to facilitate the creation and maintenance of a computerized database. • Database System: The DBMS software together with the data itself. Sometimes, the applications are also included.
ADBMS Lecture Notes 1: Prepared by Engr. Cherryl D. Cordova, MSIT 2
Evolution of Database System
ADBMS Lecture Notes 1: Prepared by Engr. Cherryl D. Cordova, MSIT
3
Ways of storing data
• Files – ancient times (1960) • Databases
– – – – Hierarchical (1970) Network (1970) Relational (1980) Object (1990)
ADBMS Lecture Notes 1: Prepared by Engr. Cherryl D. Cordova, MSIT
4
File terms
– Record • data items related to a single logical entity (e.g. a student’s information) or row in a table – Field • a place for a data item in a record (first name field in a student record) or a column in a table – File • a sequence of records of the same type...

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