Every trigonometry skill you need for GCSE Maths, explained step by step with worked examples.
Trigonometry is one of those topics that students either love or dread — and the difference almost always comes down to whether they have a clear, logical framework for approaching it. The good news is that GCSE trigonometry, even at Higher tier, follows a small set of rules that once understood properly, make every question approachable.
This guide covers everything from the very basics of SOH CAH TOA through to the sine rule, cosine rule and the area formula for non-right-angled triangles. It's written in the order you'd logically learn it, so read it through once properly rather than skipping to the bit you think you need.
All basic trigonometry at GCSE starts with right-angled triangles. The three trigonometric ratios — sine, cosine and tangent — each describe a relationship between two sides of a right-angled triangle and one of its non-right angles.
Before you can use SOH CAH TOA you need to correctly label the three sides relative to the angle you're working with. This is where a lot of students go wrong, and it's worth spending real time on this step.
Opposite and Adjacent change depending on which angle you label as your reference angle. Always label the sides AFTER you've identified which angle you're working with.
Once you've labelled the sides, SOH CAH TOA tells you which ratio to use depending on which two sides you're dealing with:
If you're finding a missing side, you'll have the angle and one other side. Identify which two sides are involved (the one you know and the one you want), then pick the ratio that connects them.
Example: In a right-angled triangle, angle A = 35°, the hypotenuse = 12 cm. Find the opposite side.
Opposite and Hypotenuse → use sin. So: sin(35°) = opposite / 12, which gives opposite = 12 × sin(35°) = 6.88 cm (to 3 significant figures).
Always write the formula first, then substitute. Don't go straight to the calculator — examiners award method marks even if your arithmetic is wrong, but only if your working is shown.
If you're finding a missing angle, you'll have two sides. Same process — identify which sides, pick the ratio. But now instead of multiplying, you use the inverse function on your calculator.
Example: opposite = 7 cm, hypotenuse = 11 cm. Find the angle.
sin(θ) = 7/11 → θ = sin⁻¹(7/11) = 39.5°
The sin⁻¹ button on your calculator is usually accessed via SHIFT + sin. Same for cos⁻¹ and tan⁻¹. Make sure your calculator is in degree mode, not radian mode — this is a surprisingly common source of wrong answers in exams.
⚠️ Always check your calculator is in DEG mode, not RAD. If your answer looks wildly wrong (like an angle of 0.69 instead of 39.5), you're almost certainly in radian mode.
The sine rule applies to any triangle — not just right-angled ones. It connects the sides and their opposite angles. You use it when you have either two angles and a side, or two sides and a non-enclosed angle (called the ambiguous case, which we'll come to).
Use the form with the side on top (a/sin A) when finding a missing side. Use the form with sin on top when finding a missing angle. You only ever use two of the three fractions at once — pick the pair where you know three of the four values.
Triangle ABC: angle A = 48°, angle B = 65°, side b = 9.2 cm. Find side a.
a/sin(48°) = 9.2/sin(65°)
a = 9.2 × sin(48°) / sin(65°)
a = 9.2 × 0.7431 / 0.9063 = 7.54 cm
Notice: you need angle C's opposite side or you need to work out angle C first. Here you have side b and angle B paired together, which is exactly what you need on the right-hand side of the equation.
The ambiguous case comes up occasionally in Higher GCSE and catches students completely off guard. It occurs when you're given two sides and an angle that isn't between them (SSA). In this situation, there can be two possible triangles that fit the given information.
When you use the sine rule to find an angle and get, say, sin(B) = 0.73, your calculator gives you one answer (around 46.9°). But there's a second possible answer: 180° − 46.9° = 133.1°. Both are valid solutions to sin(B) = 0.73. Whether both make a valid triangle depends on whether the angles still sum to less than 180° — you need to check both.
If an exam question says "find all possible values of angle B" or "show there are two possible triangles", the ambiguous case is being tested. Always check 180° − your answer as a second solution.
The cosine rule is used when the sine rule won't work — specifically when you have two sides and the angle between them (SAS), or all three sides and you want to find an angle (SSS).
The cosine rule looks intimidating but it's actually very structured. The side you're finding (or the angle opposite the side you label 'a') is always the one that appears on its own on the left-hand side.
This is something students get confused about. Here's a simple decision process:
If the angle you know is sandwiched between the two sides you know — use the cosine rule. If the angle and the sides aren't connected like that — use the sine rule. This covers 90% of exam questions.
The standard area formula — half base times height — only works when you know the perpendicular height. If you have two sides and the angle between them, you can find the area using:
Where a and b are two sides and C is the angle between them. This formula is given in the AQA formula sheet, but not always in Edexcel — check the Edexcel GCSE Maths specification and the AQA GCSE Maths specification to confirm what's provided in your exam.
Example: Two sides of a triangle are 8 cm and 11 cm. The angle between them is 57°. Find the area.
Area = ½ × 8 × 11 × sin(57°) = ½ × 8 × 11 × 0.8387 = 36.9 cm²
GCSE examiners love asking for exact trigonometric values — answers left in surd form or as fractions rather than decimals. There are six values you must know without a calculator:
These come from two special triangles: an equilateral triangle with side length 2 (which gives you the 30° and 60° values) and an isosceles right-angled triangle with legs of length 1 (which gives you the 45° values). If you derive them from those triangles rather than just memorising them, they're much harder to forget.
PaperPlus generates unlimited GCSE trigonometry questions for AQA, Edexcel and OCR, including sine rule, cosine rule and exact values — completely free.
Start Practising Free →A few errors come up so consistently in GCSE trig that they're worth addressing directly.
Not rounding correctly. Most trig questions ask for answers to 1 decimal place or 3 significant figures. Watch for this in the question — and don't round intermediate values. Keep full calculator precision throughout the working and only round the final answer.
Labelling sides relative to the wrong angle. If a question gives you two angles in a triangle and asks you to find a side, make sure you're using the angle that's actually relevant to the sides involved. In a right-angled triangle question, the reference angle is never the right angle itself.
Using SOH CAH TOA on a non-right-angled triangle. It doesn't work. SOH CAH TOA is only for right-angled triangles. If the triangle doesn't have a right angle marked, you need the sine or cosine rule.