How do I know whether to use $\sin$, $\cos$ or $\tan$ in a GCSE question?

Start by labelling the triangle relative to the angle you’re using: hypotenuse, opposite, adjacent. Then look at which sides you have been given, and which side you need to find. If the relationship involves opposite and hypotenuse, use $\sin$. If it involves adjacent and hypotenuse, use $\cos$. If it involves opposite and adjacent, use $\tan$. Write the ratio as a fraction before you rearrange, because that single line often earns a method mark even if you make an arithmetic slip later. Finally, sanity-check your answer: if you found a hypotenuse shorter than another side, something has gone wrong.

Why do my trig answers look wrong even when I use the right method?

The most common reason at GCSE is calculator mode: radians instead of degrees. Another reason is rounding too early, especially if the question later uses your value in a second step. It can also be a labelling error, where “adjacent” accidentally became “opposite” because the angle you used wasn’t the one you thought it was. Sometimes students use the correct trig ratio but rearrange incorrectly, for example dividing when they should multiply. A good habit is to keep the algebra symbolic for one line longer, like $x=\frac{20}{\cos(35^\circ)}$, before you type anything into the calculator. If you’re still unsure, practise with worked solutions and compare each line, not just the final number, using Maths Genie booklets and video solutions.

Do I need exact trig values for GCSE, and how can I remember them?

Exact values matter most for GCSE Higher because they often appear in non-calculator papers and in proof-style questions. You don’t need to memorise everything as isolated facts; you can build them from two standard triangles. The $45^\circ$-$45^\circ$-$90^\circ$ triangle gives you $\sin(45^\circ)$ and $\cos(45^\circ)$ as $\frac{\sqrt{2}}{2}$, and the $30^\circ$-$60^\circ$-$90^\circ$ triangle gives you $\sin(30^\circ)=\frac{1}{2}$ and $\cos(30^\circ)=\frac{\sqrt{3}}{2}$ (and swaps for $60^\circ$). Once those are secure, $\tan$ values follow by dividing sine by cosine. You should still practise retrieving them quickly, because in exam conditions you want recognition rather than derivation every time. The fastest way is a short daily set from Maths Genie: [Exact Trig Values exam questions (PDF)](https://www.mathsgenie.co.uk/resources/5-exact-trig-values.pdf).

How does trigonometry change from GCSE to A Level?

At A Level, you still need the GCSE fundamentals, but you use them in more algebraic and multi-step ways. Trig becomes something you manipulate, not just calculate: you solve equations, rearrange identities, and connect graphs to angles. You also move beyond right-angled triangles using the sine rule and cosine rule, which are essential for any triangle. That can feel like a big jump, but it’s usually a jump in patience rather than ability. The students who do well are the ones who keep writing clear steps and avoid skipping lines, because the algebra is where accuracy gets lost. If your GCSE SOHCAHTOA is automatic, A Level trig becomes much more manageable, and you can build from targeted practice like [A Level Trigonometric Ratios questions](https://www.mathsgenie.co.uk/a-level-year-1-questions-trigonometric-ratios.php) and [Sine and Cosine Rules & Area of Triangles](https://www.mathsgenie.co.uk/resources/104_sine-cosine-area.pdf).

GCSE Trigonometry: How to Get Better Fast

Trigonometry has a particular way of making sensible students feel silly. One minute you’re fine with angles in triangles, the next you’re staring at a diagram thinking, “Which side is opposite again?” If you’re revising for GCSE, that wobble can feel expensive: trig questions are often low-hanging marks, but only if your method is calm and repeatable. The good news is that getting better at trigonometry isn’t about being “a trig person”. It’s about building a tiny routine you can trust under pressure, then practising it until your brain stops negotiating.

A GCSE student meets SOHCAHTOA calmness

A quick checklist to get better at trigonometry (GCSE and A Level)

Use this as your five-minute warm-up before you do any trig practice:

Label the triangle: right angle, hypotenuse, opposite, adjacent.
Decide which trig ratio you need: $sin⁡\sin$ , $cos⁡\cos$ , or $tan⁡\tan$ .
Write the ratio as a fraction with your labelled sides.
Rearrange carefully (one line at a time).
Use the calculator in degrees for GCSE (check the mode).
Round appropriately: often 3 s.f. or 1 d.p. depending on the question.

For GCSE Higher, add:

Know the exact values for $0∘,30∘,45∘,60∘,90∘0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ$ .
Be fluent moving between Pythagoras and trig.

For A Level, add:

Sine/cosine rules and area of a triangle.
Solving trig equations and using identities.

You can practise these in Maths Genie’s SOHCAHTOA revision and exam questions: SOHCAHTOA (Trigonometry) -- Grade 5 and the matching booklet-style questions: SOHCAHTOA Exam Booklet.

Why trigonometry feels hard (and why it’s usually fixable)

Trigonometry is less “one topic” and more a junction. It connects geometry, algebra, calculator skills, rounding, and reading diagrams. In GCSE papers (Edexcel, AQA, OCR, Eduqas), trig often appears as a short question early on, then returns later hidden inside a longer problem (bearings, 3D shapes, compound shapes). That’s why it can feel like it comes “out of nowhere”.

But here’s the upside: because trig is method-heavy, it’s one of the easiest areas to improve quickly. If you can standardise your thinking, you can standardise your marks.

GCSE trigonometry basics: the triangle labelling habit

Before you touch $sin⁡\sin$ , $cos⁡\cos$ , or $tan⁡\tan$ , you must label the sides relative to the angle you are using.

Hypotenuse: the side opposite the right angle (always the longest side in the right-angled triangle).
Opposite: the side opposite the angle you’re working with.
Adjacent: the side next to the angle you’re working with (but not the hypotenuse).

If that sounds basic, good. GCSE trig rewards basics done correctly.

Label the sides properly, not “long-ish side”

The SOHCAHTOA anchor

sin⁡(θ)=oppositehypotenuse,cos⁡(θ)=adjacenthypotenuse,tan⁡(θ)=oppositeadjacent\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}},\qquad \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}},\qquad \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}

To consolidate, use the focused Maths Genie practice: SOHCAHTOA GCSE exam questions (PDF).

Worked example: finding a missing side (GCSE)

Question: In a right-angled triangle, the angle is $35∘35^\circ$ and the hypotenuse is $cm20\text{ cm}$ . Find the length of the opposite side $x$ .

Step 1: choose the ratio

We have opposite and hypotenuse, so use sine:

sin⁡(35∘)=x20\sin(35^\circ)=\frac{x}{20}

Step 2: rearrange

x=20sin⁡(35∘)x=20\sin(35^\circ)

Step 3: calculate

x≈20×0.5736=11.472…x\approx 20\times 0.5736=11.472\ldots

So, to $s.f.3\text{ s.f.}$ ,

cmx\approx 11.5\text{ cm}

This style is extremely common in GCSE, and it’s exactly what the Maths Genie topic and booklet questions are designed to drill.

Worked example: finding an angle (GCSE)

Question: In a right-angled triangle, the opposite side is $cm9\text{ cm}$ and the adjacent side is $cm16\text{ cm}$ . Find the angle $θ\theta$ .

Step 1: choose the ratio

Opposite and adjacent suggests tangent:

tan⁡(θ)=916\tan(\theta)=\frac{9}{16}

Step 2: inverse trig

θ=tan⁡−1(916)\theta=\tan^{-1}\left(\frac{9}{16}\right)

Step 3: calculate

θ≈tan⁡−1(0.5625)≈29.36∘\theta\approx \tan^{-1}(0.5625)\approx 29.36^\circ

So, to $d.p.1\text{ d.p.}$ ,

θ≈29.4∘\theta\approx 29.4^\circ

GCSE mark schemes love seeing the ratio written first. It proves you understood the triangle, not just the calculator.

Exact trig values: the GCSE Higher advantage

Exact values can feel like pure memorisation. But you can reduce the memory load by remembering two triangles:

The $45∘45^\circ$ - $45∘45^\circ$ - $90∘90^\circ$ triangle.
The $30∘30^\circ$ - $60∘60^\circ$ - $90∘90^\circ$ triangle.

From these, most “exact value” questions follow.

Less memorising, more patterns

For practice aligned to GCSE expectations, use: Exact Trig Values exam questions (PDF).

Key exact values to know (GCSE)

sin⁡(30∘)=12,cos⁡(30∘)=32,tan⁡(30∘)=13\sin(30^\circ)=\frac{1}{2},\quad \cos(30^\circ)=\frac{\sqrt{3}}{2},\quad \tan(30^\circ)=\frac{1}{\sqrt{3}}

sin⁡(45∘)=22,cos⁡(45∘)=22,tan⁡(45∘)=1\sin(45^\circ)=\frac{\sqrt{2}}{2},\quad \cos(45^\circ)=\frac{\sqrt{2}}{2},\quad \tan(45^\circ)=1

sin⁡(60∘)=32,cos⁡(60∘)=12,tan⁡(60∘)=3\sin(60^\circ)=\frac{\sqrt{3}}{2},\quad \cos(60^\circ)=\frac{1}{2},\quad \tan(60^\circ)=\sqrt{3}

Also:

tan⁡(0∘)=0\sin(0^\circ)=0,\ \cos(0^\circ)=1,\ \tan(0^\circ)=0

cos⁡(90∘)=0\sin(90^\circ)=1,\ \cos(90^\circ)=0

Mixing Pythagoras and trigonometry (where GCSE marks hide)

A lot of “harder” GCSE trig is just two steps: Pythagoras to find a missing side, then trig to find an angle (or vice versa). If you only practise single-step SOHCAHTOA, this is where you start bleeding marks.

Maths Genie has targeted questions for this exact blend: 3D Pythagoras and Trigonometry exam questions (PDF).

Worked example: two-step trig with Pythagoras (GCSE Higher)

Question: A right-angled triangle has hypotenuse $cm13\text{ cm}$ and one other side $cm5\text{ cm}$ . Find the angle $θ\theta$ opposite the $cm5\text{ cm}$ side.

Step 1: find the missing side using Pythagoras

Let the other non-hypotenuse side be $b$ .

5^2+b^2=13^2

25+b^2=169

b2=144⇒b=12b^2=144 \Rightarrow b=12

Step 2: choose trig ratio

Opposite is $5$ , adjacent is $12$ , so:

tan⁡(θ)=512\tan(\theta)=\frac{5}{12}

θ=tan⁡−1(512)≈22.62∘\theta=\tan^{-1}\left(\frac{5}{12}\right)\approx 22.62^\circ

To $d.p.1\text{ d.p.}$ :

θ≈22.6∘\theta\approx 22.6^\circ

That’s a very “GCSE Higher” feeling question, but the method is still just calm labelling plus two clean steps.

A Level trigonometry: what changes (and what doesn’t)

At A Level, the triangles don’t disappear, but the questions become more flexible: you’ll use trig ratios inside algebra, and you’ll meet trigonometric ratios beyond right-angled triangles.

Two particularly common A Level directions are:

Using trigonometric ratios in more involved contexts: A Level Year 1 Trigonometric Ratios questions
Using sine rule, cosine rule, and triangle area formulae: Sine and Cosine Rules & Area of Triangles (PDF)

Worked example: cosine rule (A Level and also GCSE extension)

Question: In triangle $A B C$ , $cmAB=15\text{ cm}$ , $cmAC=12\text{ cm}$ , and $∠A=60∘\angle A=60^\circ$ . Find $B C$ .

Cosine rule (side opposite $∠A\angle A$ is $B C$ ):

BC^2=AB^2+AC^2-2(AB)(AC)\cos(A)

BC2=152+122−2⋅15⋅12⋅cos⁡(60∘)BC^2=15^2+12^2-2\cdot 15\cdot 12\cdot \cos(60^\circ)

Since $cos⁡(60∘)=12\cos(60^\circ)=\frac{1}{2}$ :

BC2=225+144−360⋅12=369−180=189BC^2=225+144-360\cdot \frac{1}{2}=369-180=189

BC=189=321≈13.747…BC=\sqrt{189}=3\sqrt{21}\approx 13.747\ldots

So $cmBC\approx 13.7\text{ cm}$ to $s.f.3\text{ s.f.}$

Common GCSE trigonometry mistakes (and how to stop making them)

Mixing up opposite and adjacent

Opposite and adjacent swap depending on the angle you’re using. The triangle hasn’t changed, but your viewpoint has. Fix: put a small dot at the angle and label from that dot every time.

Using the wrong trig ratio

Students often see “angle and side” and press random buttons. Fix: say the sides out loud in your head: “I have opposite and hypotenuse, so sine.” Then write the fraction before any rearranging.

Calculator in radians

GCSE trig questions assume degrees. If your answer is nonsense, check the mode. Fix: make “DEG” part of your exam start-up ritual.

Rounding too early

If you round $sin⁡(35∘)\sin(35^\circ)$ too early, your final answer drifts. Fix: keep full calculator precision, round at the end, and follow the question’s instruction.

Forgetting units and context

Lengths need units, angles need the degree symbol. In multi-step problems, the final line often needs a sentence. Fix: treat the last line as the “mark-buying line”.

How to practise trigonometry effectively for GCSE (without burning out)

A good GCSE revision plan is rarely heroic. It’s consistent.

Start with one focused topic at a time: SOHCAHTOA (Trigonometry) then Exact Trig Values questions (PDF).
Move quickly to exam-style sets rather than endless notes: SOHCAHTOA exam questions (PDF).
Then test the skill in real context using papers: GCSE Predicted Papers (Edexcel) and broader revision lists via GCSE revision resources.

When trig appears inside mixed topics, use the mark scheme to learn what examiners reward: clear labelling, correct ratio, sensible rounding.

A triangle just wants you to label it properly

Closing: your trigonometry improvement plan (built for GCSE)

Trigonometry gets better the moment you stop treating it like a memory test and start treating it like a routine. Label. Choose. Write the ratio. Rearrange. Calculate. Round. Repeat. That’s how GCSE marks are quietly collected.

If you want a simple path, use Maths Genie as your structure: start with the SOHCAHTOA (Trigonometry) revision topic, practise using the SOHCAHTOA exam questions (PDF), add confidence with Exact Trig Values questions (PDF), then pressure-test yourself using GCSE Predicted Papers and wider GCSE revision resources. Keep the mark schemes close, use video solutions when you get stuck, and let your revision planner do the heavy lifting of consistency.

Do that, and trigonometry stops being the topic that “turns up”. It becomes the topic you’re quietly hoping turns up -- because it’s yours.