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

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Graphs of Trigonometric Functions

Graphs of trigonometric functions

  • The Trigonometric Functions Sin, Cos and Tan all have special periodic graphs that you need to be able to sketch and remember
  • You’ll need to know their properties and how to sketch them to solve equations and for transforming trig functions

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

Sketching trigonometric graphs

Graphs of Trigonometric Functions Diagram 2, A Level & AS Level Pure Maths Revision Notes

Using trigonometric graphs

  • By sketching the graph you can read off all the solutions in a given range (or interval)
  • Your calculator will only give you the principal value
  • You should recognise any values/angles associated with exact values
  • You should be able to spot the pattern of solutions using the symmetry and periodicity of the graph

 

Graphs of Trigonometric Functions Diagram 3, A Level & AS Level Pure Maths Revision Notes

Examiner Tip

  • Always sketch with a pencil and draw a smooth curve and pay attention to the key features of each graph:
    • Where it crosses the x and y axes
    • How often it repeats
    • Whether it is symmetrical
  • Remember, when answering exam questions that ask for solutions, a sketch will help ensure you give all the appropriate solutions for a given interval.

Worked example

Graphs of Trigonometric Functions Example Solution, A Level & AS Level Pure Maths 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.