• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. 12
  13. 13
  14. 14
  15. 15
  16. 16
  17. 17

sunrise over newyork

Extracts from this document...


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


                                         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.


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.


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.


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.


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.


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.


  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-Connect Disc

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Extended Essay- Math

    m-��2��� ��&T'$�IMJæd2g���i��:�0�/:|����xeo�\ib�l...G�X��(c)og�jq� �}�wkh1/2���<Þ¢q���Õk����;;�"o߬1/4E�"��k��"g�'��<X}6�~����1�'�Æ��{(r)��p��+��o^1/2�y->=2#�!i��1/4��"O= [_��\t_r_����Mh���{�j���kY?�?Ϭ֣×on"o�m�m��|�%�E�j�Z�V�N�3/43/4c��@%Å�@��������� �<3/41/21/2^1/21/21/2Y��7�����+v���(tm)�Ét'���7���� ��s�c�b pHYs �� IDATx�{�UU�� Y^R�B#** (c)��%@1#�0@!`�"C0�RJ@����2j�#��h�"""���@�D�4�1/4+���:��e���/k������k��Y���}5:p��B@TA q���-"��# .(c)} "�B@\2=B@�Kj! �- BG�"��'�B@� �%���3! "�����B q� t�L! .(c)= "�B@\2=B@�Kj! �- BG�"��'�B@� �%���3! "�����B q� t�L! .(c)= "�B@\2=B@�Kj! �- BG�"��'�B@� z�gv#���-[�1/4���?���o���K/1/2����S>�"�8�"O>(tm)�֭[7k֬�(c)(r)...��@#��&{�|� �<�����(r)]��SO�O;�48`Ó¦M�8��� S...��47m����Oi�"w�Ν;*k��#�(��...�K�cÑ£O>�dݺu+V�x���<�� :���/})�, {]1/2z5�٥K-!C����#|! R3!��'���-[�hÑ5k�9ç " �/���Z��(r)"�BI�Q�3��m B�!

  2. Derivative of Sine Functions

    The line of the tangent becomes steeper and steeper as the points move from left to right within-2to-2+1,-+1to-+1,-+1 to 1,+1 to +1,+1to 2. �The gradient is positive in the domain of :[-2,-+1[, ]-+1, +1[, ]+1,2] The gradient is negative in the domain of::]-+1,-+1[, ]+1, +1[. 3when c =2 f(x) =sin(x+2)

  1. Using regression analysis to solve a real time problem

    3 85 25 1 6 80 36 0 5 75 54 0 14 70 45 0 10 70 38 1 9 75 57 Number of Accidents vrs Vehicle Maintenance It is observed that there is a negative linear relationship between the number of accidents and the age of driver.

  2. Investigating Sin Functions

    Conjecture - Part 1 Finally, we reach the conjecture. Initially, I would have assumed that as A increases, the graph would stretch vertically and make the wave longer vertically, and that as A decreases, the graph would shrink vertically and make the wave shorter vertically.

  1. Mathematics Higher Level Internal Assessment Investigating the Sin Curve

    We can use a similar method for the rest of the equations: From this it can be seen that , and . This would mean that the amplitude of the graph would be , causing the original graph to be stretched inwards by units.

  2. A logistic model

    Mathematics HL Type II Portfolio: Creating a logistic model International School of Helsingborg - Christian Jorgensen un?1 ? (?1? 10?5 )(u n?1 )2 ? 1.6(u n?1 ) ? H ? ??(?1?10?5 )(u n?1 )2 ? 1.6(u n?1 )?? ? u n?1 ? H ? 0 ? (?1?10?5 )(u )2 ?

  1. Mathematics (EE): Alhazen's Problem

    This will give the point along the circumference must one ball must be aimed at in order for it to strike the other after rebounding off the edge. Another method introduced by Michael Drexler and Martin J. Gander in their essay "Circular Billiards" involves using a different geometric derivation10.

  2. While the general population may be 15% left handed, MENSA membership is populated to ...

    However, in the chi-squared calculations done by hand () in Table G, the values were used to three significant figures (see Calculation of Expected Values, page 11) for more accurate data. Degrees of Freedom The degree of freedom dictates the acceptable amount of variance in the final statistical calculation.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work