Temperature+Model

Ashling Cook, Mary Mendenhall, Billy Mylin, Tyler Loy

Problem #1: Create an annual temperature model using the sine or cosine function for a city of your choice. Fully explain the components of your model, compare the predictions from your model to the actual temperatures from the data set you used and include a use of your temperature model.

**Average Highs: ** January: 34ºF February: 39ºF March: 45ºF April: 51ºF May: 61ºF June: 72ºF July: 77ºF August: 75ºF September: 69ºF October: 58ºF November: 43ºF December: 35ºF

On Graphs: y axis= Average Temperature in degrees F x axis= Month, one tick mark=one month

Sine Graph of Average Highs:
Equation: y=21.03*sin(.54x+-2.34)+55.65 Amplitude= 21.03 Period= 2 π/.54 Horizontal Shift= -2.34 Vertical Shift=55.65



Sine Graph of Average Highs with Average Highs Plotted:


**Average Lows: ** January: 7ºF February: 11ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">March: 19ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">April: 25ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">May: 33ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">June: 41ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">July: 46ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">August: 46ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">September: 39ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">October: 29ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">November: 17ºF <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">December: 9ºF

Sine Graph of Average Lows:
Equation: y=19.31*sin(.51x+-2.14)+26.66 Amplitude=19.31 Period= 2 π/.51 Horizontal Shift= -2.14 Vertical Shift= 26.66

Sine Graph of Average Lows with Average Lows plotted:


The Sine Graph was a good model for the actual average highs and lows as both the average highs and lows matched the graphs well.