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GCSE Maths: Exact Trig Values

Recall and use the exact values of sin, cos and tan for key angles. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

GeometryHigher tierAQA · Edexcel · OCR · Eduqas

What you need to know

The concepts examiners test on exact trig values, and what each one is really asking.

Recall the exact values of sin, cos and tan at 0, 30, 45, 60 and 90 degrees
Derive them from the two standard triangles
Use exact values in non-calculator trigonometry
Leave answers in surd form when asked

Where marks get lost

The exam technique that separates a correct method from a correct answer.

  • Writing a decimal such as 0.866 when the question asks for an exact value
  • Swapping sin and cos at 30 and 60 degrees — sin 30 is 1/2 and cos 30 is root 3 over 2
  • Forgetting that tan 90 is undefined rather than zero
  • Leaving a surd in the denominator when the answer should be rationalised

Exact Trig Values questions students ask

Is Exact Trig Values on the Foundation paper?

No — Exact Trig Values is a Higher tier topic, so it appears on Higher papers only.

What should I know before starting Exact Trig Values?

It builds on Pythagoras and trigonometry and Surds and Fractions. If those feel shaky, practise them first — Exact Trig Values questions assume them.

What is the most common mistake in Exact Trig Values?

Writing a decimal such as 0.866 when the question asks for an exact value.

Which exam boards cover Exact Trig Values?

All four we support — AQA, Edexcel, OCR and Eduqas. GCSE Maths subject content is set by the DfE, so the topic is common to every board; what changes is the paper structure and the grade boundaries.