• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Math Portfolio - Weather Analysis

Extracts from this document...

Introduction

Introduction

        The purpose of this mathematics assignment is to explore the cosine function transformations with the data collected from the average temperature of a city in Ontario. Using www.weatherbase.com, we found average temperatures from the city of our choice. In my case, I selected Bloomfield, Ontario. The data points collected form a cosine function by nature that is already transformed and translated.

Cosine Equation

y=AcosB(x - C)+D

image00.png

image01.png

Breakdown

In the function, A represents the amplitude. The amplitude is a vertical dilation of either compression or stretch. It directly affects the size of the wavelengths in the function. In this situation, the amplitude is the range of the temperature over a twelve-month period.

...read more.

Middle

A period is defined as the time for one full cycle to take place in the graph. The period of this graph is 12 since the data was collected over the span of a year, or 12 months.

In this function, the B-value represents the horizontal dilation. The horizontal dilation is the horizontal stretch or compression. This affects how long it takes for the data to be collected. Since the period is 12 months, we can calculate 2π/12 to find the value for B. In this situation, B is equal to π/6.

In this function, the phase shift, or variable C, is a horizontal translation to the left or right. The value is simply 1 (or -1 when inserted into the parent equation).

In this

...read more.

Conclusion

image03.png

        In the southern hemisphere, the temperatures are much more intense. The function will not be inverted since the temperatures are so high. All the variables will, again, remain similar, but the amplitude is very small. The function is close to being a straight line since the temperature is, for the most part, the same the whole year.image04.png

...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�]y�N�O��<F�䦢��-K�2"�kX�]�HV��-"X�d�"È°h�Bd.�ZnQH��"�)C�q#���{1/4��1/4g�g�}>��{�>{?��Ù��g?;Ï7�� �C�N�(c)L���'���x'ߣ���D��g -E���(c)6 �Y ��G �=jx�MH~�"�QH~��j'�u�x'ߣ���D��g -E���(c)6 �Y ��G �=jx�MH~�"`W(r)\(c)S�N�~�"�f�����/|�hѢ�5���7 _'aHKK"z�j��7"LÓ³g�?o�]1/4x1��f�'�f��"J!��o�"W�|��}��5�jݺu"w�~����� &=i�1/2k�~>�Y0 " �"W_�dI'"E-z��1/2{7j�(@ï¿½ï¿½ï¿½ï¿½ï¿½Ç ï¿½lÙ²e(tm)2en�>}z��6lX"vm�#�g"4_|�ERRR"v�'""#|;���]���p�[ "Э[7�V?���L����1/2{�h�d��OMM}���+W(r)��g�4:t�g��ÇgffN�8�- ����X( �" "�é§.[��ҥKÛ·o3f��"�~�z0_����lÅ=z��ر#���*�ܹs1/2z�9r�2=ifΜ 0�/X� �"V]�� I��n�Æ�h���h�"�2��[�~}��5k��jÖ¬(tm)���Kv��常��u�1/4�'MBBµk�0:�T(c)R��-�$�-�'(tm)�-�"'O-(Q�bÅYYYG�-��� Vi���7������?q�ıc�ڴi�9u�T0�S�N�h.Z��\�rI"c�g���"����U"V�TJJ�s�=7i�$ �-WfΜ9��y�l_{�5,:�A`�֭�}~�G6�z ��K-, ����R�J9�|nn�'#G�*^1/4�������Ì�1/4��/�m(�'�Vx(tm)9�'_^�P2"`+$���2s" /$�1/4��dD�VH~[�e�D@^H~ymC�d@ �]�t�?�mJ-.=�|��D(r)�[#3Q0�ҥ�z�/1/2Ν;kw�{A�"�v"\h�(tm)O+(c)@�ժU�é§ï¿½;�1/2 ��k;'c��... D"�2�{��y�A�"�X��c��)��(r)]"�ٳG�-�~�YyAB 0cÆbÅaO~�B...��m۶�7.D:�"�]h4�,����c��7P&�|l�Uc���/�-�(" l�e�e! ��͢��L��2Y������fQD@&H~(tm)�AY��@H~�`�(" $�L� ,D@ $�@�Y� '_&kP" '_ �,��"�/"5( ��/lEdB��-�"...D��6�"2!@��d �B"@� �E(tm) �e�e!

  2. Ib math HL portfolio parabola investigation

    EXAMPLE: Graph 19 and Table6: Showing how D = 0 for a cubic polynomial. x1 x2 x3 x4 x5 x6 D=|(x1+x4+x5)-(x2+x3+x6)| -1.09148 -0.90022 0.454128 0.538254 2.553225 2.446093 0 Table 7: Showing how the value of D = 0 for a cubic polynomial.

  1. Math Portfolio: trigonometry investigation (circle trig)

    Quadrant 2-(-,+) sin ?=y/r =- cos ?=x/r=-1 tan ?=y/x= - Quadrant II The value of y equals a positive number in the quadrant 2 and the value of r equals a positive number as mentioned beforehand. Likewise, when the value of y is divided by the value of r, a

  2. Artificial Intelligence &amp;amp; Math

    IT Background of the Issue Laptop usage in U.S. schools increased by 43% in the 2001-2002 school year (Suryaraman, 2002). Last year, 15% of school districts in America were participating in a laptop initiative (Corcoran, 2002). Although desktop computers far outnumber laptops in the school environment, an increasing trend in

  1. Stellar Numbers math portfolio

    An expression for the 7th term is S7= S6+ (S6-S5) + 10 (, where 10 is the constant second difference). Again, this was derived through the pattern noticed above where essentially the sum of each row is equivalent to the next Sn value, or at any value of n, where

  2. Maths Modelling. Crows love nuts but their beaks are not strong enough to ...

    After looking at the list I immediately ruled out the linear, the quadratic as well as the sine regression because it was highly unlikely that they would provide a curve of best fit for the data points. This left me with only two options which were the exponential regression and the power regression.

  1. Maths Project. Statistical Analysis of GCSE results at my secondary school summer 2010 ...

    10 40 m 40 53 O'D 8 28 m 28 52 Ol 11 34 m 34 51 Or 9 46 f 46 50 Pa 9 40 m 40 49 Ph 10 40 m 40 48 Po 10 28 m 28 47 Po 11 46 m 46 46 Re 8 40

  2. Modelling the H1N1 Epidemic in Canada

    the factors that might affect the propagation or hindrance of a disease and devise methods to properly limit or eliminate a disease within a population. The SIR Model One way Epidemiology uses mathematics to predict an epidemic is through the use of compartmental models.

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