Lesson 4

In Try This 2, you saw that it is reasonable to use a sinusoidal curve of best fit to represent a set of data and make predictions for the October 7 to 11 data. However, you need to be careful about when to use a sinusoidal curve of best fit. Not all periodic data can be modelled nicely using a sinusoidal curve; the distribution of the scatter plot will help you decide if a sinusoidal model is reasonable.

Interpolation will usually yield a reasonable result, but you need to be very careful with extrapolation. The data pattern will need to be consistent to use extrapolation, and small errors in the model can create large extrapolation errors if the prediction is far outside the data range.

Self-Check 1

1. A clock with a pendulum sits above a counter. The height of the pendulum above the counter is measured at various time intervals.
   
   

   Time (s)	0	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0
   Height (cm)	22.0	16.0	10.0	16.0	22.0	16.0	10.0	16.0	22.0

   1. Plot the data.
   2. Sketch a curve of best fit for the data.
   
   

   Answers

2. What is the period of the graph? What does it represent in this scenario? Answers
3. Use your graph to predict the height of the pendulum at
   1. 1.7 s
   2. 12.5 s
   
   Answers
4. How accurate do you expect your predictions from question 3 to be? Explain. Answers