1. Homework Questions? Discuss with the people around you. Do not turn in Homework yet… You will do it at the end of class.

2. Trigonometric Functions – Day 2 1.6

3. Goal Given a set of data, I will find the sinusoid function and graph the function using the calculator.

4. Example An oven is set to bake at temperature of 350  F. The oven takes a while to heat up, then it remains at a fairly constant temperature. The following temperatures are taken at different times (t minutes) after the oven is turned on. Use a sine or cosine function to model the temperature of the oven at time t.

5. Copy this table in your notes time (t minutes) 202428323640444852 temperature (degrees Farenheit) 350354.9347.8346.1353.9352.2345.1350354.9

6. What does this look like? Start by entering the data into your calculator, choosing an appropriate window, and graphing it.

7. What do we need to do?

8. Vertical Translation The vertical translation is the average of the maximum and minimum values. vertical translation = (354.9 + 345.1)  2 = 350

9. Amplitude The amplitude is the distance from the horizontal axis (the vertical translation) to a maximum or minimum value, so: Amplitude = 354.9 - 350 = 4.9

10. Period By looking at the table, it would appear that the function will have maximum values when t = 24 and t = 52. It also looks like the function completes two cycles between these times (because it looks like there is another max somewhere between t=36 and t=40). 52-24=28. 28 divided by 2 cycles =14 We will estimate the period to be 14 minutes.

11. Horizontal Translation The horizontal translation is the y value of the first max minus one-fourth of the period. 14÷4, or 3.5. The horizontal translation for our sine curve would be 24 - 3.5= 20.5

12. Put it all together

13. Check your equation Graph your equation to check if it is a close fit with the data.

14. You are ready! Now you can do question 24 on page 52. When you are done, turn in the 1.6 homework assignment.