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Average Monthly Temperatures

By Kaylee LoPresto

Purpose

The purpose of this project is to see how trigonometric functions can be applied in the real world, and in this project, we are using sinusoidal graphs and functions to compare the average monthly temperatures of three different cities around the world.

Sinusoidal graphs

Tucson, AZ

Tucson, AZ

Average Temperature Chart - Surat, Gujarat, India

Surat, Gujarat, India

Berryville, VA

Berryville, VA

Berryville, VA

Sinusoidal Function For Berryville

Sinusoidal Function

F(x)= 23.0sin{(π/6)x-2.1{+63.0

Analysis-

Amplitude

23

Period

12

Phase Shift

12.6/π

Sinusoidal Graph for Berry ville

The best time to travel to Berry ville is during July since that is when Berry ville is the warmest and is still not too hot to vacation in.

Sinusoidal Graph

Tucson, AZ

Tuscon, AZ

Sinusoidal Function for Tucson, AZ

Sinusoidal Function

G(x) = 17.5sin(π/6x-2.1)+83.5

Analysis-

Amplitude

17.5

Period

12

Phase shift

12.6/π

Sinusoidal Graph for Tucson, AZ

The best time to go to Tucson is during April since this month offers reasonable weather. Unlike July when the weather is in the 100 degrees. In April there are reasonable hotel rates.

Sinusoidal Graph

Surat, Gujarat

Surat, Gujarat, India

Sinusoidal Function for Surat, Gujarat

Sinusoidal Function

T(x) = 5.4sin(π/6-2.1)+92.8

Analysis

Amplitude

5.4

period

12

Phase shift

12.6/π

Sinusoidal Graph for Surat

The best time to visit Surat is in January because of the monthly average temperature, it is not as hot as in July. In January there will be little rainfall and clearer skies since Surat's Monsoon season occurs during the summer.

Sinusoidal Graph

Graph comparison

All 3 graphs

Sine regression for each city

Berryville

F(x)= 23.4sin(0.5x-1.9)+62.6

Tucson

g(x)= 17.9sin(0.5x-2.2)+83.9

Surat

t(x)= 4.5sin(1.0x-2.7)+ 92.0

Sine regressions

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