Transformations of Trigonometric Functions (CIE A Level Maths: Pure 1)

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Transformations of Trigonometric Functions

Transformations of trigonometric functions

  • You should already have a good idea about translating, stretching and reflecting basic functions (see Transformations of Functions)
  • The basic principles are exactly the same for transforming any trigonometric graph
    • y = n cos x gives a vertical stretch or squash
    • y = sin nx gives a horizonal stretch or squash
    • y = tan (x + c) gives a horizonal translation

    Transformations of Trigonometric Functions Diagram 1a, A Level & AS Level Pure Maths Revision Notes

 

Transformations of Trigonometric Functions Diagram 1b, A Level & AS Level Pure Maths Revision Notes

 

Transformations of Trigonometric Functions Diagram 1c, A Level & AS Level Pure Maths Revision Notes

Examiner Tip

  • Always sketch with a pencil and draw a smooth curve.
  • When you sketch the transformation of a graph, be sure to indicate the new coordinates of any points that are marked on the original graph.
  • Try to indicate the coordinates of points where the new graph intersects the axes. 

Worked example

5-2-2-transformations-of-trigonometric-functions-example-solution

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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.