GCSE Exact Trig Values: Complete Revision Guide

GCSE exact trig values are one of the most reliable sources of marks in your maths exams. They appear on Paper 2 and Paper 3 (both calculator and non-calculator), and the questions are almost always straightforward — if you know the values.

The good news? There are only 15 values to learn (five angles, three functions each). Commit them to memory and you are practically guaranteed marks every single exam series. This guide covers exactly what your GCSE specification requires, gives you the complete table, walks through real exam-style questions, and shares the best ways to lock these values into your long-term memory.

What the GCSE Specification Requires

All three major exam boards — AQA, Edexcel, and OCR — require Higher Tier students to know the exact values of sine, cosine, and tangent for the following angles:

0°
30°
45°
60°
90°

This is explicitly stated in the GCSE Mathematics specification under the trigonometry section. You are expected to recall these values without a calculator and use them within longer problems. Foundation Tier students may encounter simpler versions, but the full set is firmly a Higher Tier requirement.

Knowing these values means you can answer recall questions instantly and apply them confidently in multi-step problems involving right-angled triangles, trigonometric identities, and exact-answer questions.

The Complete GCSE Exact Values Table

Here is the complete table of exact trigonometric values you need for GCSE. Keep this table in your head and you will never be caught out. Both the exact (fraction/surd) and approximate decimal forms are shown.

Angle	sin θ	cos θ	tan θ
0°	0	1	0
30°	½ (0.5)	√3⁄2 (0.866)	1⁄√3 (0.577)
45°	1⁄√2 (0.707)	1⁄√2 (0.707)	1
60°	√3⁄2 (0.866)	½ (0.5)	√3 (1.732)
90°	1	0	Undefined

Tip: Notice the pattern — the sin values from 0° to 90° are 0, ½, 1⁄√2, √3⁄2, 1. The cos values are the same sequence in reverse. Spotting this symmetry cuts your memorisation work in half.

You can also write 1⁄√2 as √2⁄2 and 1⁄√3 as √3⁄3 — both forms are accepted in GCSE mark schemes. Use whichever you find easier to remember. For the full reference table with rationalised denominators, see our dedicated page.

How These Appear in GCSE Exams

GCSE exam questions on exact trig values typically fall into three categories: direct recall, combining values, and application in context. Here is one example of each, with full worked solutions.

Example 1 — Direct Recall

Without a calculator, find the exact value of sin 60°.

[1 mark]

Solution

sin 60° = √3⁄2

This is pure recall. One mark, a few seconds of writing. You either know it or you do not — there is no method to fall back on without a calculator.

Example 2 — Combining Values

Show that cos 30° + tan 45° = (√3 + 2)⁄2

[3 marks]

Solution

Step 1: Write down the exact values.

cos 30° = √3⁄2

tan 45° = 1

Step 2: Add the two values using a common denominator.

√3⁄2 + 1 = √3⁄2 + 2⁄2

Step 3: Combine.

= (√3 + 2)⁄2 ✓

“Show that” questions require you to demonstrate every step. Do not skip straight to the answer — examiners want to see the recall and the algebraic manipulation.

Example 3 — Application

A right-angled triangle has a hypotenuse of 10 cm and an angle of 30°. Find the exact length of the side opposite the 30° angle.

[2 marks]

Solution

Step 1: Identify the relevant ratio. We have the hypotenuse and want the opposite side, so use sine.

sin 30° = opposite⁄hypotenuse

Step 2: Substitute the exact value.

½ = opposite⁄10

Step 3: Solve.

opposite = 10 × ½ = 5 cm

The key word in the question is “exact.” Whenever you see it, the examiner is telling you to use exact trig values, not a calculator approximation.

Quick Memorisation Tips

There are several proven methods for memorising GCSE exact trig values. Here are the most popular ones:

The finger trick: Hold up your left hand. Number your fingers 0 to 4 (thumb = 0, little finger = 4) for angles 0°, 30°, 45°, 60°, 90°. For sin, take the square root of the finger number and divide by 2. For cos, count from the other side.
The pattern method: Write the sequence 0, 1, 2, 3, 4. Square root each, then divide by 2. This gives sin 0° through sin 90°: 0, ½, √2⁄2, √3⁄2, 1. Reverse the sequence for cosine.
Spaced repetition: Test yourself daily with flashcards or a quiz app. Short, frequent sessions beat long cramming sessions every time.

For a deeper dive into each of these techniques, read our full guide on how to remember exact values.

Common GCSE Mistakes

After years of marking and tutoring, the same errors come up again and again. Avoid these and you are already ahead of most students.

Mistake 1: Swapping sin 30° and sin 60°. This is by far the most common error. Remember: sin 30° = ½ (the smaller angle gives the smaller value for sine). Sin 60° = √3⁄2. If in doubt, think: 30° is a small angle, so sine should be small.

Mistake 2: Forgetting tan 90° is undefined. Students often write 1 or 0. Tangent is sine divided by cosine, and cos 90° = 0, so you would be dividing by zero. The answer is undefined — write it clearly and you will pick up the mark.

Mistake 3: Mixing up degrees and radians. At GCSE level, you work almost exclusively in degrees. If a question says 30°, do not convert to π⁄6. Save radians for A-Level. Stick with the degree values in the table above unless told otherwise.

Mistake 4: Not rationalising the denominator. Some mark schemes expect √2⁄2 rather than 1⁄√2. Both are correct, but if the question says “give your answer in the form a⁄b”, you may need to rationalise. Practise both forms so neither catches you off guard.

How to Practise Effectively

Knowing the values is only half the battle. You need to be able to recall them under pressure, in timed conditions, without hesitation. Here is a revision plan that works:

Daily quick-fire recall (2 minutes): Test all 15 values from memory. Write them out on a blank table. If you get stuck on any, that is the one to focus on. Do this every day in the week before your exam.
Timed practice questions (10 minutes): Attempt exam-style questions under timed conditions. Aim for the three types shown above: recall, combining, and application. Past papers from AQA, Edexcel, and OCR all have examples.
Spaced repetition: Do not cram the night before. Instead, practise a little each day over 2–3 weeks. Research consistently shows that spacing out your revision leads to significantly better long-term retention.
Use an interactive quiz: Our free quiz lets you practise every exact value with instant feedback. It tracks which values you struggle with and focuses on those automatically.

Exam tip: In the exam, spend the first minute of the trigonometry question writing out the values you need in the margin. This takes the pressure off your working memory and reduces silly mistakes.

For more context on why memorising these values matters beyond just passing GCSE, see our article on why we need to memorise exact values in mathematics.

Ready to Lock In Your Exact Values?

The fastest way to commit GCSE exact trig values to memory is to practise recalling them repeatedly. Our free interactive quiz tests you on every single value, adapts to your weak spots, and tracks your progress over time. A few minutes a day for two weeks is all it takes to make these values second nature.

Stop losing easy marks. Start practising now and make exact values the simplest part of your GCSE maths exam.

Practise GCSE Exact Values Now