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sunrise over newyork

Extracts from this document...

Introduction

IB Standard Level Type II

Math Portfolio

Sunrise over New York

Student Names: Nam Vu Nguyen

Set Date: Thursday, December 20, 2007

Due Date: Wednesday, January 09, 2008

School Name: Father Lacombe Senior High School

Teacher: Mrs. Gabel

I CERTIFY THAT THIS PORTFOLIO ASSIGNMENT IS ENTIRELY MY OWN WORK

                                         Nam Vu Nguyen: ___________________________________

IB Standard Level - Type II - Math Portfolio

Sunrise over New York

Mathematics is a study of the concepts of quantity, structure, space and change. It is a type of science that draws conclusions and connections to the world around us. Mathematicians would call math a science of patterns and these patterns are discovered in numbers, space, science, computers, imaginary abstractions, and everywhere else. Mathematics is also found in numerous natural phenomena’s that occurs around us. Today math is used all around us and is applied to many educational fields, through this people have become inspired to discover and make use of their mathematical knowledge which will then lead to entirely new disciplines. Math is present in wherever there are difficult problems that involve quantity, structure, space or change; such problems appear in various forms such as commerce, land measurement and especially astronomy.

The purpose of this paper is to examine the data on the times of the sunrise over New York, over a period of 52 weeks in one year. Sunrises are the beginning of a new day, when the first part of the sun appears over the horizon in the east. Since the dawn of mankind man himself have pondered on the mysteries of the Sun itself. Civilizations of the past have attempted to explain the reason why the sun rose in the morning and set in the night. This eventually led to creation of monuments around the world such as the Egyptian Pyramids, Stonehenge, and the Ancient Mayan Temples.

...read more.

Middle

a, b, c and d.

The variable “a” is the amplitude of the function. The amplitude is accountable for determining the vertical stretch of the trigonometric functions. Amplitude is the distance from the center line (equilibrium) of the function to either the maximum or minimum points. The value of a can be found out by the following formula, where the difference of the maximum value and the minimum value is divided by two.

image06.png

The next variable “b”, is responsible for the horizontal stretch of the sine function. It represents the number of cycles that a trigonometric graph has within a span ofimage07.png. Therefore the formula to calculate the variable “b” is where image07.pngis divided by the period of the graph.

image08.png

The variable “c”, determines the number of units of a function’s horizontal translation. If image09.pngthen there is a “c” unit’s horizontal translation to the left. If the image10.pngthen there is a “c” units horizontal translation to the right.

The variable “d”, determine the “d” units of the function’s vertical translation. If the image11.pngthen there is a “d” units vertical translation up. If the image13.pngthen there is a “d” units vertical translation down. It is determined by the formula where the sum of the maximum value and the minimum value is divided by two.

image14.png

After discussing the purpose of the trigonometric values and how to calculate them, we will now set out to determine the functions that can model the data. The following values will now be calculated for a cosine function as follows:

“A” value = image06.png = image15.png = image16.pngor image17.png

“B” value = image08.png = image18.png = image19.png or ≈image20.png

“C” value = 0, this is because the graphs have no phase shifts. Cosine functions have y-intercepts that begin at another number other than zero for their “x” value.

“D” value = image14.png = image22.png ≈image23.png or image24.png

...read more.

Conclusion

rd and September 29th.Therefore, the days when there was more than twelve hours of daylight are between March 23rd and September 29th of 2003.

To conclude the assessment, identified and discovered information from data given to us and solved the problems present to us by using technology that was granted to us. The purpose of the assignment is now complete as all necessary questions are resolved and steps were taken to correctly identify the problem, assess it and accomplish it. the portfolio demonstrated that all the data that was used and processed have the potential to solve no only have real life applications, but also the mysteries that surrounds them. The student using their knowledge of graphs, cosine and sine functions, transformations, and graphing on not only the TI-83 Plus calculator, but also the media present to them was successful in solving the task given to them on the Sunrise of New York.

Reference:

  1. Microsoft Office 2003 XP Professional
  2. http://www.cic-caracas.org/vanas/vanascontent/handouts/davis2.pdf
  3. http://aa.usno.navy.mil/data/docs/RS_OneYear.php
  4. http://www.xuru.org/rt/TOC.asp
  5. http://www.libs.uga.edu/ref/chicago.html
  6. Student based notes on Trigonometry and Functions.
  7. Texas Instruments        TI-83 Plus

        TI-GRAPH LINK USB

        TI-Connect Disc

...read more.

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