GCSE & IGCSE maths practice

Exact trig values questions and answers

You need to know some trig values without a calculator: $\sin 30° = \cos 60° = \tfrac{1}{2}$ , $\sin 60° = \cos 30° = \tfrac{\sqrt{3}}{2}$ , $\sin 45° = \cos 45° = \tfrac{\sqrt{2}}{2}$ , $\tan 45° = 1$ , $\tan 30° = \tfrac{1}{\sqrt{3}}$ and $\tan 60° = \sqrt{3}$ . They come from two special triangles. Type surds like √3/2.

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

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Where exact trig values comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°, and of tan θ for 0°, 30°, 45° and 60°.
Cambridge IGCSE (0580)	Extended only: know the exact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90°.

The method

45°: a right-angled isosceles triangle with sides 1, 1, √2.
30° and 60°: half an equilateral triangle, sides 1, √3, 2.
Read the ratio from the triangle with SOH CAH TOA.

Exact trig values questions

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Warm-up

Question 1Warm-upFoundation

Write down the exact value of $\sin 30°$ .

Question 2Warm-upFoundation

Write down the exact value of $\tan 45°$ .

Exam-style

Question 3Exam-styleFoundation

Write down the exact value of $\cos 60°$ .

Question 4Exam-styleFoundation

Write down the exact value of $\cos 30°$ .

Question 5Exam-styleFoundation

Write down the exact value of $\tan 60°$ .

Question 6Exam-styleFoundation

Write down the exact value of $\sin 45°$ .

Challenge

Question 7ChallengeFoundation

Without a calculator: a right-angled triangle has hypotenuse 8 cm and an angle of $60°$ . Find the side adjacent to the $60°$ angle.

Question 8ChallengeFoundation

Work out the exact value of $\sin 60° \times \cos 30°$ .

Common mistakes

Swapping sin 30° and sin 60°.
Writing tan 30° as √3.
Using a calculator on a non-calculator paper.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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