Are exact trig values on the Edexcel formulae sheet?

No, and that is the trap. The Higher Exam Aid issued with each 1MA1 paper carries the three right-angled ratios, the sine rule, the cosine rule and the area formula (1)/(2)ab C, but it prints no numerical values. 30^ , 45^ and the rest are still straight recall, which is why a question can ask for them for one mark.

Which exact trigonometric values do I have to learn for Edexcel Higher?

Spec reference G21 asks for and at 0, 30, 45, 60 and 90 degrees, and at 0, 30, 45 and 60 degrees. That is fourteen values in total. 90^ is not on the list because it has no value: the adjacent side has shrunk to zero and a calculator returns an error.

Are exact trig values on the Foundation paper?

No. G21 is Higher tier only, so Foundation candidates are never asked for them, even though they meet the same three ratios under G20. It is one of the shorter Higher-only spec points, which makes it worth learning properly: a mark for writing down 60^ = sqrt(3) is as good as any other mark on the paper.

What is the easiest way to remember the exact trig values?

Draw the two triangles instead of memorising a table. An equilateral triangle of side 2 cut down the middle gives a right-angled triangle with sides 1, sqrt(3) and 2, which produces every value at 30 and 60 degrees. A square of side 1 cut along its diagonal gives sides 1, 1 and sqrt(2), which produces the 45 degree values. The 0 and 90 degree values come from imagining the triangle flattened or stood upright.

Exact Trigonometric Values - Edexcel GCSE Higher Maths

Typically 1-4 marks per paper, concentrated on Paper 1 · Spec 1MA1

Spec reference G21 on Edexcel's 1MA1 is a memory list and nothing else: the exact values of $\sin \theta$ and $\cos \theta$ at $0^\circ$ , $30^\circ$ , $45^\circ$ , $60^\circ$ and $90^\circ$ , together with the exact value of $\tan \theta$ at $0^\circ$ , $30^\circ$ , $45^\circ$ and $60^\circ$ . Tangent stops at $60^\circ$ because $\tan 90^\circ$ has no value. G21 is Higher tier only, so a Foundation candidate never meets it, and it is the one part of the trigonometry content that cannot be looked up during the exam.

That last point is the whole reason this topic exists as a separate page. The Exam Aid issued with every 1MA1 paper for the 2025 to 2027 windows prints the three right-angled ratios, the sine rule, the cosine rule and $\text{Area} = \frac{1}{2}ab\sin C$ . It does not print a single numerical value, so a question that hands you $\sin 60^\circ$ to work with hands you nothing you can read off the insert. Edexcel asks for it in three shapes: a one-mark 'write down the exact value of $\cos 30^\circ$ ' near the front of Paper 1, a two- or three-mark combination such as $10\cos 30^\circ + 3\tan 30^\circ$ to be written in the form $a\sqrt{b}$ , and a triangle whose angle happens to be 30, 45 or 60 degrees where the answer must be left as a surd. The values also turn up on Papers 2 and 3, because the word 'exact' in a stem overrules the calculator sitting on the desk.

Almost every dropped mark here is one of two things. The first is writing $\sin 60^\circ = \frac{1}{2}$ , which is the value of $\sin 30^\circ$ ; the pair get swapped more than any other. The second is converting a correct surd into 0.866 and putting that on the answer line, which loses the accuracy mark on a question that asked for an exact value. The fix for both is the same and takes under a minute at the start of the paper: sketch half an equilateral triangle of side 2 and an isosceles right-angled triangle with two sides of 1, label them, and read every value you need off your own sketches rather than out of memory under pressure.

Worked example

Triangle ABC has a right angle at B. Angle BAC =

60^\circ

and AB = 6 cm. Do not use a calculator. Work out the exact perimeter of triangle ABC. Give your answer in the form

a + b\sqrt{3}

cm, where

a

and

b

are integers.

[4 marks]

AB is next to the $60^\circ$ angle and BC faces it, so BC is the opposite and AB the adjacent: $\tan 60^\circ = \frac{BC}{6}$ . Since $\tan 60^\circ = \sqrt{3}$ , $BC = 6\sqrt{3}$ cm.
M1: tan chosen for opposite over adjacent, with $\tan 60^\circ$ recalled as $\sqrt{3}$
AC faces the right angle, so it is the hypotenuse: $\cos 60^\circ = \frac{6}{AC}$ . Since $\cos 60^\circ = \frac{1}{2}$ , $AC = 6 \div \frac{1}{2} = 12$ cm.
M1: dividing by the half rather than multiplying by it, so AC comes out as 12 and not 3
Perimeter $= AB + BC + AC = 6 + 6\sqrt{3} + 12$ .
M1: all three sides added, the surd term left alone
Collect the two integers: perimeter $= 18 + 6\sqrt{3}$ cm, so $a = 18$ and $b = 6$ .
A1: $18 + 6\sqrt{3}$ ; do not turn it into 28.4, the question said exact

Practice questions

These are original questions in Edexcel 1MA1 Higher style, and all of them are meant to be done with the calculator face down. Where an answer is a surd you are asked for the integers inside it, or given four forms to choose between, because a square root sign cannot be typed into a box. Every triangle is described in words, so sketch it and mark the right angle before you pick a ratio.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [1 mark]

Write down the exact value of tan 30 degrees.

Answer options for question 1
$\sqrt{3}$ $\frac{\sqrt{3}}{2}$ $\frac{\sqrt{3}}{3}$ $\frac{1}{2}$
Question 2 Warm-up [2 marks]

Triangle PQR has a right angle at Q. PQ = 6 cm and QR = 6 cm. Work out the size of angle QPR, in degrees.

Your answer (fractions like 1/2 are fine)
Question 3 Exam pace [2 marks]

Which of these is equal to $\frac{1}{\sqrt{3}}$ ?

Answer options for question 3
$\frac{\sqrt{3}}{3}$ $\frac{\sqrt{3}}{2}$ $\sqrt{3}$ $\frac{1}{3}$
Question 4 Exam pace [2 marks]

$x$ is an acute angle and $\tan x = \sqrt{3}$ . Work out the value of $x$ , in degrees.

Your answer (fractions like 1/2 are fine)
Question 5 Stretch [3 marks]

The diagonal of a square is 8 cm long. The length of a side of the square can be written as $a\sqrt{b}$ cm, where $a$ and $b$ are integers and $b$ is as small as possible. Write down the value of $a$ and the value of $b$ .

a = b =
Question 6 Stretch [5 marks]

PS is perpendicular to the straight line SR, and PS = 6 cm. Q is a point on SR between S and R. Angle SPQ = 30 degrees and angle SPR = 60 degrees. The length of QR can be written as $a\sqrt{b}$ cm, where $a$ and $b$ are integers and $b$ is as small as possible. Write down the value of $a$ and the value of $b$ .

a = b =

Common mistakes examiners see

Swapping the 30 and 60 degree pair, writing $\sin 60^\circ = \frac{1}{2}$ or $\cos 30^\circ = \frac{1}{2}$ . In an area calculation that single slip turns $12\sqrt{3}$ into 12.

Anchor them to the half-equilateral triangle with sides 1, $\sqrt{3}$ and 2. The short side of 1 faces the $30^\circ$ angle, so the $\frac{1}{2}$ belongs to $\sin 30^\circ$ and to $\cos 60^\circ$ . Sketch that triangle in the margin before you start rather than trusting recall.
Replacing the surd with a decimal: giving $\cos 30^\circ$ as 0.866 or an area of $12\sqrt{3}$ as 20.8 when the question says 'exact' or 'in the form $a\sqrt{b}$ '.

The word exact in an Edexcel stem means no rounding anywhere, so the answer line has to carry a fraction or a surd. Rounding costs the accuracy mark even when every earlier line is right.
Expecting the values on the Exam Aid and hunting for them mid-question, or worse, guessing because the insert only shows $\sin A = \frac{a}{c}$ .

The insert gives the ratios, the sine and cosine rules and $\frac{1}{2}ab\sin C$ , and no numbers at all. Write out the nine values at 30, 45 and 60 degrees on the front of the paper in the first minute, while nothing else is competing for your attention.
Multiplying by the fraction instead of dividing by it: from $\sin 30^\circ = \frac{4}{x}$ writing $x = 4 \times \frac{1}{2} = 2$ rather than $x = 4 \div \frac{1}{2} = 8$ .

When the unknown sits underneath, it changes places with the trig value. Then size-check: $x$ here is a hypotenuse, so it cannot come out shorter than the 4 cm side.
Losing a factor of a half in the area formula, so $\frac{1}{2} \times 8 \times 10 \times \sin 60^\circ$ is written as $40\sqrt{3}$ instead of $20\sqrt{3}$ .

There are two halves in play, the one in the formula and the one inside $\frac{\sqrt{3}}{2}$ . Work out $\frac{1}{2} \times 8 \times 10 = 40$ on its own line first, then multiply by $\frac{\sqrt{3}}{2}$ to get $20\sqrt{3}$ .

Frequently asked questions

Are exact trig values on the Edexcel formulae sheet?: No, and that is the trap. The Higher Exam Aid issued with each 1MA1 paper carries the three right-angled ratios, the sine rule, the cosine rule and the area formula $\frac{1}{2}ab\sin C$ , but it prints no numerical values. $\sin 30^\circ$ , $\cos 45^\circ$ and the rest are still straight recall, which is why a question can ask for them for one mark.
Which exact trigonometric values do I have to learn for Edexcel Higher?: Spec reference G21 asks for $\sin \theta$ and $\cos \theta$ at 0, 30, 45, 60 and 90 degrees, and $\tan \theta$ at 0, 30, 45 and 60 degrees. That is fourteen values in total. $\tan 90^\circ$ is not on the list because it has no value: the adjacent side has shrunk to zero and a calculator returns an error.
Are exact trig values on the Foundation paper?: No. G21 is Higher tier only, so Foundation candidates are never asked for them, even though they meet the same three ratios under G20. It is one of the shorter Higher-only spec points, which makes it worth learning properly: a mark for writing down $\tan 60^\circ = \sqrt{3}$ is as good as any other mark on the paper.
What is the easiest way to remember the exact trig values?: Draw the two triangles instead of memorising a table. An equilateral triangle of side 2 cut down the middle gives a right-angled triangle with sides 1, $\sqrt{3}$ and 2, which produces every value at 30 and 60 degrees. A square of side 1 cut along its diagonal gives sides 1, 1 and $\sqrt{2}$ , which produces the 45 degree values. The 0 and 90 degree values come from imagining the triangle flattened or stood upright.

Exact Trigonometric Values - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics