GCSE Trigonometry exam-style questions
Use Clevolab for GCSE exam-style practice in trigonometry. This page shows what the topic covers, what skills the current set targets, and a few real examples from the reviewed question bank.
About this topic
Clevolab treats trigonometry as repeated practice with explanation, not just answer checking. This page is designed to make the topic legible before you open the app.
The current GCSE set covers triangle problems, angle reasoning, trigonometric ratios, and standard trigonometric methods. 35 reviewed questions currently published for this page.
What you can practise
- Sine, cosine, and tangent
- Right-angled triangle methods
- Sine rule and cosine rule
- Angle problems
- Practical geometry links
Real sample questions from the current set
These examples come from the reviewed questions currently stored for this topic. They are here so the page shows the actual flavour of Clevolab, not just a summary.
Sample question
Solve $\cos x=-\tfrac{\sqrt{3}}{2}$ for $0^\circ\le x<360^\circ$.
- A30°, 330°Answer option
- B60°, 300°Answer option
- C120°, 240°Answer option
- D150°, 210°Correct answer
Why this answer is right
$\cos x=\tfrac{\sqrt{3}}{2}$ at $30^\circ$. Negative cosine occurs in quadrants II and III, giving $180^\circ\pm30^\circ=150^\circ,210^\circ$.
Use a reference angle of $30^\circ$ because $\cos30^\circ=\tfrac{\sqrt{3}}{2}$.
Sample question
In a triangle, two sides are $8\,\mathrm{cm}$ and $11\,\mathrm{cm}$ with included angle $64^\circ$. Find the opposite side.
- A18.9 cmAnswer option
- B13.4 cmAnswer option
- C10.4 cmCorrect answer
- D3.0 cmAnswer option
Why this answer is right
Use the Cosine Rule: $c^2=8^2+11^2-2\cdot8\cdot11\cos64^\circ$. This gives $c\approx10.4\,\mathrm{cm}$.
For side $c$ opposite the $64^\circ$ angle, apply the Cosine Rule.
Sample question
In a triangle, two sides are $7\,\mathrm{cm}$ and $9\,\mathrm{cm}$ with included angle $60^\circ$. Find the third side to $2$ d.p.
- A$8.19\,\mathrm{cm}$Correct answer
- B$11.40\,\mathrm{cm}$Answer option
- C$13.89\,\mathrm{cm}$Answer option
- D$9.00\,\mathrm{cm}$Answer option
Why this answer is right
Use the Cosine Rule for an included angle: $c^2=a^2+b^2-2ab\cos C$. With $a=7$, $b=9$, $C=60^\circ$, $c^2=49+81-126\times0.5=67$, so $c=\sqrt{67}\approx8.19\,\mathrm{cm}$.
The Cosine Rule applies with two sides and the included angle. $$c^2=a^2+b^2-2ab\cos C$$ Substitute $a=7$, $b=9$, $C=60^\circ$ and $\cos60^\circ=0.5$: $$c^2=7^2+9^2-2\cdot7\cdot9\cdot0.5=49+81-63=67$$ Take the square root: $$c=\sqrt{67}\approx8.19\,\mathrm{cm}$$ This is between $7$ and $9$, which is reasonable for a $60^\circ$ angle.
How this page fits into Clevolab
Clevolab is broader than any one exam mode. GCSE and A-level pages are useful entry points, while the wider project is about sharpening understanding through repeated topic practice.