Trigonometry Exact Values (CIE A Level Maths: Pure 1)

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Trigonometry Exact Values

Exact values

  • In trigonometry some values of sin, cos and tan are “nice”
  • For example sin 30° = ½, tan 45° = 1
  • We can find those associated with the angles 30°, 45° and 60° using SOHCAHTOA on isosceles and equilateral triangles

Exact Values Notes Diagram 1, A Level & AS Maths: Pure revision notes Exact Values Notes Diagram 2, A Level & AS Maths: Pure revision notes 

  • sin, cos and tan values for 30°, 45° and 60° should be recalled easily
  • Memorise either the actual values or how to work them out from the triangle
  • sin, cos and tan for , 90°, 180° should also be very familiar
  • They can be recalled using the relevant trigonometric graph (see Graphs of Trigonometric Functions)

Exact values and radians

  • All of the above applies to radians as well as degrees
  • Here is a table of all exact values including radians (see Radian Measure)

5-4-2-exact-values-notes-diagram-3-1

How do I find exact values of other angles?

  • Exact sin, cos and tan values of multiples of 30°, 45°, 60° can also be found
  • This is a combination of recalling the basic values and using the graph

Exact Values Notes Diagram 4, A Level Maths: Pure revision notes

Examiner Tip

  • Draw the triangles for sin, cos and tan of 30°, 45° and 60° on the exam paper so that you can then use them as many times as you need throughout the paper.

Worked example

Exact Values Example Diagram, A Level & AS Level Pure Maths Revision Notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.