Sinusoidal Models (DP IB Applications & Interpretation (AI)): Revision Note

Sinusoidal Models

What are the parameters of a sinusoidal model?

• A sinusoidal model is of the form

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• 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 period is  (in degrees) or  (in radians)

• The c represents the phase shift

  • This is a horizontal translation by c units

• 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