5.9.1 Modelling with Trigonometric Functions

Modelling with trigonometric functions

• Various real-life situations can be modelled using trigonometric functions
• You need to be able to interpret the equations used in the model
• If you need to identify maximum or minimum values of a formula, remember the bounds of the sin and cos functions:
  • -1 ≤ sin x ≤ 1
  • -1 ≤ cos x ≤ 1

  

• You may need to simplify trigonometric expressions to make the behaviour of an equation clearer

 

 

• You may also need to discuss the period of an equation
  • The period is often indicated by T
  • For a periodic function in x like sin or cos, the period is how much x has to change by for the function to go through one complete cycle

 

• For functions of the form cos (qx+ r) or sin (qx + r) the period T is: