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A LevelMaths: Pure 1CIERevision Notes3. Trigonometry3.5 Modelling with Trigonometric Functions3.5.1 Modelling with Trigonometric Functions

Modelling with Trigonometric Functions (CIE A Level Maths: Pure 1)

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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

 

Model Trig Illustr 1, A Level & AS Maths: Pure revision notes

  • 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

 Model Trig Illustr 3_period graph, A Level & AS Maths: Pure revision notes

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

 

Model Trig Illustr 3_period form, A Level & AS Maths: Pure revision notes

 

Model Trig Illustr 4, A Level & AS Maths: Pure revision notes

Examiner Tip

  • The variable in these questions is often t for time.
  • Read the question carefully to make sure you know what you are being asked to solve.

Worked example

Model Trig Example, A Level & AS Maths: Pure revision notes

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    Lucy

    Author: Lucy

    Expertise: Head of STEM

    Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels. Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. Lucy has created revision content for a variety of domestic and international Exam Boards including Edexcel, AQA, OCR, CIE and IB.