DfE statement G21 · Geometry and measures

Exact trigonometric values

Both tiersNon-calculator

Exact trigonometric values is content statement G21 of the DfE GCSE mathematics subject content, in the geometry area. It is on both tiers, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°." (statement G21). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement G21

Tier

Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.

Calculator

This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.

Common mistakes

Swapping sin 60° and cos 60°. sin 60° is √3/2 and cos 60° is ½.
Giving tan 90° a value. It is undefined.
Answering with a rounded decimal when the question asks for the exact value, which on Paper 1 scores nothing.

Formulae for this statement

The trigonometric ratios (right-angled triangles)sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adjYou must know this

Sample questions (10 of 30)

G21 · Exact trigonometric valuesQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Geometry and measures

G21

Intermediate

A tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.

💡 Hints:

Foundation worksheet Higher worksheet Foundation geometry and measures practice Higher geometry and measures practice

Nearby statements

G1Geometric terms, notation and diagrams G2Ruler and compass constructions and loci G3Angle facts, parallel lines and polygons G4Properties of triangles and quadrilaterals

Questions people ask

Is exact trigonometric values on Foundation or Higher?

Both. It is Foundation content, so it can be asked on either tier.

Can I use a calculator for exact trigonometric values?

Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.

What is the single most common mistake here?

Swapping sin 60° and cos 60°. sin 60° is √3/2 and cos 60° is ½.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Geometry and measures at Foundation or at Higher.