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Let the Sun Shine

Student Worksheet 2




Name __________________________      Period_______      Date_______________



This activity continues with the daylight data that you collected previously. You should be in a group with the same students you worked with when the data collection took place.

You will show the plot of your data and this time you will come up with an equation to model this data so you can find the daylight time for any given day of the year.

  1. Run the program DAYLIGHT that contains the data you collected from the website.

  2. Turn on the plots and graph the data.

  3. It might appear that this data looks like an upside down parabola, but think about the fact that this data is cyclical, it will repeat and repeat. You only see one cycle because you only plotted the data for one year's worth of daylight times. How long is each daylight cycle? _______

  4. What type of function do you think would best model this data? _____________________ Why? ______________________________________________________________________________________________

  5. The next step is selecting the "parent" function to model the data. In this lesson you will fit the data to the Cosine family of functions. The reason for choosing cosine over sine is that it is easier to fit cosine to data since cosine has its maximum value on the y-axis and that value will be easy to find.

  6. On the homescreen, store in the value of zero for A, B, C, and D. Make sure that your calculator is in radian mode. Type in the cosine family equation into Y1 as shown at the right. Turn the function off by pressing ENTER with the cursor on the equal sign.

  7. To review the parts of the cosine family, fill in what each of the variables A, B, C, and D represent.

    A __________________    B __________________    C __________________    D _________________

  8. The plan is to find each value, store it in, and then graph. Let's start with A, the amplitude of the function.

    This is found by taking _ of the maximum - the minimum values on the graph. Day 172 approximately the longest day of the year and 356 is approximately the longest day of the year. Trace along the plot until you come to each of these days and record the daylight times. __________ __________ Compute the amplitude and store this value in for A on the calculator. A = _______.

  9. Did you get the same values as the other members of your group? ______ Why or why not? _______________________________________________________________________________________

  10. The location with the greatest amplitude is.___________________________________________________.

  11. The location with the least amplitude is______________________________________________________.

  12. The next value we will find the horizontal shift to the right. Trace back to the maximum value. This x-value should correspond with longest day, 172. Since we are graphing this as a cosine curve, the graph will need to shift to the right, 172 units. Store in 172 for C.

  13. You already know that the length of one cycle is 365. The fundamental period of cosine is 2. If you divide 2by 365 you will obtain what portion of the graph you will see in 2. Store that value you in for B. B = _______.

  14. Before we worry about the vertical shift (D), turn on Y1 and press ZoomStat to view the graph. If you do not see anything but the plot, you must make an adjustment to the vertical shift. Change your WINDOW to show a y-min of -10. When you return to the graph window you will see where the function is. Try storing difference values in for D until you have the correct value. Press ZoomStat again to view the graph and the correct function. D = ________.

  15. Write your complete equation using the values for the four variables: y = ___________________________

  16. Go back to the WINDOW and change x-max to 730. This is model two years. Press GRAPH.

  17. Press 2nd TRACE and then VALUE. Ask for the 500th day of the year. How many hours of daylight are on that day? ___________

  18. What day in the year does 500 correspond with? _______ Check that daylight hours on that day. _______

  19. Is amplitude the only value that is different with respect to the equations in your group? Why or why not? _______________________________________________________________________________________

  20. LINK over the equations that each member of the group found to each calculator. You should then have equations in Y1, Y2, Y3, and Y4. Graph these with the same viewing window. Compare and contrast the graphs with what you have learned in this lesson. List as many items as you can below. Review these with the members in your group.

Similarities           Differences

 

 

 

 

 

 


The Integrating Technology into Math Instruction webpages project is partially funded by a grant from The Boeing Company. Integrating Technology into Math Instruction is a project of +PLUS+ and is displayed on the Los Angeles Educational Partnership Learning Exchange. +PLUS+ is an initiative of the Los Angeles Educational Partnership.
Updated June 2000