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Modelling with Trigonometric Functions (OCR A Level Maths A) : Revision Note

Roger B

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Roger B

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OCR Maths A: PureAQA Maths: PureEdexcel Maths: Pure

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

Model Trig Illustr 2, 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 Tips and Tricks

  • 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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    Roger B

    Author: Roger B

    Expertise: Maths

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.