Modeling Weather Using Sinusoidal Graphs

Modeling Weather Patterns Using Trig

You are tasked with modeling the weather of a city of your choosing (anywhere in the United States) as a sine or cosine function. Colorado cities and the example city (Birmingham, AL) are off limits , so do some exploring, and choose a new place to explore! :)

Tasks: 1. First, pick your city. Then use this website to find the weather data from every month. You will track the monthly high AND low temperatures and graph both. 2. Take your 24 values and put them into a Google Sheets file. You will graph your weather patterns using Google Sheets for average low temperatures and average high temperatures. Your x-axis should be each month (so, time, t), and your y-axis should be a reasonable scale for you to properly assess your temperatures. 3. Then you will have to use your plotted points to write a sine or cosine function that best represents the climate of your chosen city. Keep in mind that I have provided you with equations for amplitude and the principle axis. Those might just come in handy, especially when you’re working with less than perfect scenarios. :) 4. You will write a minimum 5 sentence summary (full sentences) explaining your experience with this project. Feel free to include some explanations of your work that you felt may not be correct, things you struggled with, things you felt were helpful, etc. Remember, you have access to the sentence stems document to help you. :)

The Details:

1. Here is the template I have prepared for you to use for this project. Please make a copy of it and use it. Please do not make any large alterations to the prepared document, either.

2. I do not want your Sheets File. Copy & Paste your completed graph into your Google Doc. Submit ONLY the Google Doc. Here is a video on how to make graphs in Google Sheets.

3. There will be several screenshots that need to be included in your submission. Please do not take a picture with your phone and upload it. The quality makes grading difficult. IF YOU DO NOT KNOW HOW TO DO A SCREENSHOT ON YOUR DEVICE, GOOGLE IT: “how to do a screenshot on a _____.”

4. You will need to use “Equation Writer” in Google Docs to show your work/write your equations. The Equation Writer can be found under “Insert,” and the only symbols you will need are and the fraction symbol . can be found under the “greek symbols” category after selecting the Equation Writer. The fraction symbol will be under “math operations,” the fourth button. Please see this video for a rundown of how to use Equation Writer.

Rubric:

0-2	3-4	5-6	7-8
No or Minimal Attempt made	Partially Complete, with some accurate calculations shown.	Mostly Complete, most accurate calculations shown.	Complete, all accurate calculations shown.

In Order to Write the Correct Equation, You Have to Find the Following Values:

Amplitude: Find the amplitude (a-value) of this curve. Think about this for a minute. Using a wave's max & min... how do you figure out the amplitude? Make sure to show how you found the amplitude!

Period: Find the period and use it to find the b–value (frequency) of this curve. Think about this for a minute. This curve repeats every 12 months. Use that to help you find b. Make sure to show how you found b.

Hint: When t reaches 12, (bt) must begin to repeat….

Phase Shift (horizontal shift): The temperature is likely at its lowest (minimum) in Jan when t = 0. Use that fact to find the c–value. Make sure to show how you found c.

Hint: When t = 0, sin(bt + c) must be at its minimum. When is the sin t at its minimum?

Midline (Sinusoidal Axis): You are likely not in a city where the lowest temperature happens to be 0°. That means you also need to find the midline, the d-value.

After finding all of these values, you will be able to write the function of your city’s weather patterns for the high average and the low average. Therefore, you should have TWO functions.

↓See Ms. Reichel’s Example Project below↓

Keep in mind this is NOT showing you the work.

You must show your work, though. ;)

[Name]

Average Temperatures in Birmingham, AL

Compiled Data & Graphed using Excel/Sheets:

Some Thoughts: I noticed a pattern in my city where the highest temperatures occurred in the same month, and the lowest temperatures occurred in the same month. That proved to be an interesting experience when calculating the curve function. I also immediately noticed that the weather patterns in my city reflected the cosine curve when I first graphed the data.

Calculations:

Amplitude (a): [work & answer using Equation Writer]	Period →Frequency (b): [work & answer using Equation Writer]
Phase Shift (c): [work & answer using Equation Writer]	Midline (d): [work & answer using Equation Writer]

Avg High:

Avg Low:

[Final Reflection]