You can write a trigonometric function to model a situation.
Temperature Cycles The table gives the average temperature in your town x days after the start of the calendar year
Day of Year | 16 | 47 | 75 | 106 | 136 | 167 | 198 | 228 | 258 | 289 | 319 | 350 |
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Temperature (°F) | 33 | 35 | 42 | 52 | 62 | 72 | 77 | 76 | 69 | 58 | 48 | 38 |
Think | Write |
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Make a scatter plot of the data in the table. | |
The cosine function has the form
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One complete cycle takes 365 days. |
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The maximum point of the curve is (198, 77). | phase shift:
vertical shift: |
Write the function in the form
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To check your answer, graph the function with the scatter plot to see if it is a good fit. |