Sample Questions

1. Which of the following rules best match this graph? Explain.
   
   1. y = cos x
   2. y = cos 4x
   3. y = sin 4x
   4. y = sin x
      
2. What is the period and amplitude of y = 3cos 2 x?
   
3. What would be a good model for this data?
   

Sample Response

1. Since the graph starts at (0, 0) it's a sine curve. Also, there are 4 periods in 2π, so that makes c. y = sin 4x the right choice.
   
2. The period is π and the amplitude is 3 for the graph of y = 2cos 3x.
   
3. Let x = day number and y = daylight hours.
   It looks like the data doesn't start in the middle range of daylight hours so I think cosine is a good choice.
   Yet cosine normally starts on the top and this graph starts on the bottom. That means I'll have y = - cos x.
   It takes 360 days to repeat, so in degree mode y = - cos x is looking good since it takes 360° for cos to repeat.
   The amplitude looks like 3 since it's about 6 hours from minimum to maximum. That'll give me y = -3cos x.
   
   Yet the center line of the data is about 13 hours. So y = -3cos x + 13 is my rule (in degree mode).