AQA A Level Maths: Pure复习笔记5.4.2 Trigonometry Exact Values

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

5.4.2-Exact-Values-Notes-Diagram-1 5.4.2-Exact-Values-Notes-Diagram-2

  • 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 0°, 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)


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


Exam 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