IB DP Maths: AA HL复习笔记3.5.3 Modelling with Trigonometric Functions

What can be modelled with trigonometric functions?

• Anything that oscillates (fluctuates periodically) can be modelled using a trigonometric function
  • Normally some transformation of the sine or cosine function
• Examples include:
• Notice that the x-axis will not always contain an angle
  • In the examples above time or number of days would be on the x-axis
  • Depth of the water, temperature or vertical height would be on the y-axis

What are the parameters of trigonometric models?

• A trigonometric model could be of the form
  • The bigger the value of b the quicker the function repeats a cycle
• The c represents the horizontal shift
• The d represents the vertical shift
  • This is the principal axis

What are possible limitations of a trigonometric 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 value of d 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