IB DP Maths: AI SL復習筆記2.3.5 Sinusoidal Models
Sinusoidal Models
What are the parameters of a sinusoidal model?
- A?sinusoidal model?is of the form
The?a?represents the?amplitude?of the function
- The bigger the value of?a?the bigger the?range?of values of the function
- The?b?determines the?period?of the function
- The bigger the value of?b?the quicker the function repeats a cycle
- The?d?represents the?principal axis
- This is the line that the function fluctuates around
What can be modelled as a sinusoidal model?
- Anything that oscillates (fluctuates periodically)
- Examples include:
- D(t) is the depth of water at a shore?t?hours after midnight
- T(d) is the temperature of a city?d?days after the 1st January
- H(t) is vertical height above ground of a person?t?second after entering a Ferris wheel
What are possible limitations of a sinusoidal model?
- The amplitude is the same for each cycle
- In real-life this might not be the case
- The function might get closer to the principal axis over time
- The period is the same for each cycle
- In real-life this might not be the case
- The time to complete a cycle might change over time
Exam Tip
- Read and re-read the question carefully, try to get involved in the context of the question!
- Sketch?a graph of the function being used as the model, use your GDC to help you and focus on the given domain
Worked Example
a)Write down the depth of the water at midnight.
b)Find the minimum water depth and the number of hours after midnight that this depth occurs.
c)Calculate how long the water depth is at least 13.5 metres each day.
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