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Average Monthly Temperatures Sinusoidal Graphs Project

By Bliss Bodawala

Math Analysis

Block 2

11/26/2018

Bliss Bodawala, Math Analysis, Block 2

"Purpose"

Title and Overview

Slides

The purpose of this project was 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.

Selected Cities:

~ Berryville, VA

~ Tucson, AZ

~ Surat, Gujarat, India

The Problem

Average Temperature Chart for Berryville

Average Temperature Chart for Surat, Gujarat

Average Temperature Chart for Tucson

Link~

https://www.weather-atlas.com/en/india/surat-climate#temperature

Link ~

https://www.usclimatedata.com/climate/berryville/virginia/united-states/usva0061

Link ~

https://www.usclimatedata.com/climate/tucson/arizona/united-states/usaz0247

Berryville, Virginia

City #1 Content Slide

Sinusiodal function and graph

Sinusoidal Function for Berryville, VA

f(x) = 23.0sin{(π/6)x-2.1}+63.0

Analysis of Equation:

Amplitude: 23

Period: 12

Phase Shift: 12.6/π

Sinusoidal Function Graph for Berryville, VA

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

Link to Graph on Desmos: https://www.desmos.com/calculator/r2tyhqlccb

Tucson, Arizona

City #2 Content Slide

Sinusoidal Function for Tucson, AZ

g(x) = 17.5sin(π/6x - 2.1)+83.5

Sinusoidal Function

Analysis of Equation:

Amplitude: 17.5

Period: 12

Phase Shift: 12.6/π

Sinusoidal Graph

Sinusoidal Graph for Tucson, AZ

The best time to go to Tuscon is during April since this month offers reasonable weather(has more sunny skies and warm/tolerable weather), unlike July, which has a avg. high greater than 100 degrees Fahrenheit, and in April there are also reasonable hotel rates in Tucson.

Link to Graph on Desmos ~ https://www.desmos.com/calculator/a0bz5itc2y

Surat, Gujarat (India)

City #3 Content Slide

Sinusoidal Function for Surat, India

t(x) = 5.4sin(π/6-2.1)+92.8

Sinusoidal Function

Analysis of Equation:

Amplitude: 5.4

Period: 12

Phase Shift: 12.6/π

Sinusoidal Graph for Surat, Gujarat (India)

Sinusoidal Graph

The best time to visit Surat is during January because that month is when its average temperature is not too hot like in July, with an average temperature of around 97 degrees Fahrenheit, and in January, there will be little rainfall and clearer skies since Surat's Monsoon Season occurs during the summer(warmest months).

Link to Graph on Desmos ~ https://www.desmos.com/calculator/lrx5jnb6qo

Graph Comparison for All 3 Cities

Comparison Slide

Key ~

Blue = Surat, India

Purple = Tucson, AZ

Red = Berryville, VA

SINe REGression for Each City

Summary Slide

Berryville, VA ~ f(x)= 23.4sin(0.5x-1.9)+62.6

Tucson, AZ ~ g(x) = 17.9sin(0.5x-2.2)+83.9

Surat, India ~ t(x) = 4.5sin(1.0x-2.7)+92.0

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