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Bliss Bodawala, Math Analysis, Block 2
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
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
f(x) = 23.0sin{(π/6)x-2.1}+63.0
Analysis of Equation:
Amplitude: 23
Period: 12
Phase Shift: 12.6/π
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
g(x) = 17.5sin(π/6x - 2.1)+83.5
Analysis of Equation:
Amplitude: 17.5
Period: 12
Phase Shift: 12.6/π
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
t(x) = 5.4sin(π/6-2.1)+92.8
Analysis of Equation:
Amplitude: 5.4
Period: 12
Phase Shift: 12.6/π
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
Key ~
Blue = Surat, India
Purple = Tucson, AZ
Red = Berryville, VA
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