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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.

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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

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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

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