Exact Trig Values (AQA GCSE Maths): Revision Note

Exact Trig Values

What are exact values in trigonometry?

• For certain angles the values of sin θ, cos θ and tan θ can be written exactly

  • This means using fractions and surds

• You are expected to know the exact values of sin, cos and tan for

  • 0°, 30°, 45°, 60°, 90°, 180° and their multiples

How can I remember these exact trig values?

• Look at patterns in the table

  • Note the values of sin θ from 0° to 90° match cos θ in reverse, from 90° to 0°

  • Some people remember sin θ using the trick which simplifies to

• Two special right-angled triangles below can help you to find the exact values for 30º, 45º and 60º

  • Remember that by rationalising the denominator,

• The trig graphs can help you to remember the exact values for 0º and multiples of 90º

How do I use exact trig values?

• You may come across trig questions in a non-calculator question

• In trig calculations, substitute in the exact trig values and solve as usual

  • E.g. Solve the equation

    • Replace with to give

    • Then you can solve for

• On trig graphs, you may be expected to find a coordinate

  • E.g. The coordinates lie on the graph , find

    • will be equal to

    • The exact value of is

    • Therefore