# Math Portfolio - Weather Analysis

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 , 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

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. By calculating subtracting the maximum and minimum temperatures, you will fall upon the middle value. This value is 13.5. Considering the first values of the graph are in the negatives – obviously because of the fact that January and February are winter months – the A value is going to be negative.

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 ...