Trigonometry: JAMB Mathematics Questions, Answers & Notes

What Trigonometry covers in the JAMB Mathematics syllabus

Trigonometry relates angles and sides. In a right-angled triangle, SOH-CAH-TOA: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent (= sin θ/cos θ). Learn the standard values: sin 30° = ½, cos 60° = ½, tan 45° = 1, sin 60° = cos 30° = √3/2, tan 60° = √3. The key identity is sin²θ + cos²θ = 1. For non-right triangles use the sine rule (a/sin A = b/sin B = c/sin C) or cosine rule (a² = b² + c² − 2bc cos A). Angles of elevation and depression, and bearings (measured clockwise from North), are common applications.

For Trigonometry, JAMB expects you to be able to:

• Use the sine, cosine and tangent ratios in right-angled triangles
• Recall standard values and the identity sin²θ + cos²θ = 1
• Apply trigonometry to angles of elevation/depression, bearings, and the sine/cosine rules

Key facts & revision notes: Trigonometry

These are the recurring points our Trigonometry questions test — revise them until each feels automatic, then practise the questions above to lock them in.

• sin 30° = 1/2 (a standard trigonometric value).
• SOH: sine = opposite ÷ hypotenuse.
• CAH: cosine = adjacent ÷ hypotenuse.
• TOA, and equivalently tan θ = sin θ / cos θ.
• Using a 3-4-5 triangle (or sin²+cos²=1): cos θ = 4/5.
• Height = 10 sin 60° = 10 × (√3/2) = 5√3 m.
• The fundamental identity: sin²θ + cos²θ = 1.
• Height = 20 tan 45° = 20 × 1 = 20 m.
• The angle of depression equals the angle of elevation (they are alternate angles).
• The sine rule: a/sin A = b/sin B = c/sin C.
• The cosine rule: a² = b² + c² − 2bc cos A.
• The smaller angle is opposite the shorter side (6).
• tan = opposite/adjacent = 6/8.
• Bearings are measured clockwise from North; due East is 090°.
• Using the 3-4-5 triangle, sin θ = 3/5.
• tan θ = opposite/adjacent.
• √(13² − 5²) = √144 = 12 m.
• height = 30 tan 30° = 30/√3 = 10√3 m.
• Hypotenuse = 5, so sin = opposite/hyp = 3/5.
• Due South is a bearing of 180°.
• Due West is a bearing of 270°.
• The hypotenuse faces the right angle and is longest.

Worked examples

Three Trigonometry questions with the answer and a short explanation, so you can see how the topic is set before you practise the full set.

How Trigonometry is tested in JAMB Mathematics

Our Trigonometry bank holds 40 questions (17 easy, 16 medium, 7 hard). JAMB Mathematics typically returns to Trigonometry year after year, so steady practice on this topic is high-value revision. Questions are multiple-choice with four options, and at UTME pace you get roughly 40 seconds each — which is why timed practice matters.

How to answer Trigonometry questions

Work the stem first and predict the answer before you look at the options; then eliminate the ones that contradict the key facts above. Watch for “which is not…”, “all of the above” and “except” style stems, which are where rushed candidates lose easy marks on Trigonometry. If a calculation or a precise definition is involved, work it from first principles rather than guessing from a half-remembered rule. When two options look right, re-read the stem for the qualifier that separates them — JAMB rarely repeats an option by accident. If you are still unsure, eliminate the two weakest choices to lift your odds, flag the question, and move on; never burn a full minute on one Mathematics item when the exam gives you about forty seconds each. Then come back to flagged questions with whatever time remains. The single most reliable way to get faster at Trigonometry is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Trigonometry

The errors that cost marks on Trigonometry are usually careless rather than conceptual: misreading a negative stem, confusing two similar terms, or rushing a definition you actually know. Candidates also over-rely on “expo” and last-minute cramming instead of understanding the topic — which fails the moment JAMB rephrases a familiar idea. Treat every option as a claim to be checked against the facts above, keep your working tidy for any calculation, and don’t change a considered answer on a hunch. Above all, revise Trigonometry actively by answering questions, not just by re-reading notes — recall under time is what the exam rewards.

Frequently asked questions

Is Trigonometry part of the JAMB Mathematics syllabus?

Yes. Trigonometry is a recognised topic in the JAMB Mathematics syllabus, covering use the sine, cosine and tangent ratios in right-angled triangles. You should be able to recall its key facts and apply them to multiple-choice questions.

How many Trigonometry questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Trigonometry questions in our free bank, each with the correct answer and a worked explanation. You can practise them untimed or as a timed test.

What are the most important points to know about Trigonometry?

Trigonometry relates angles and sides. In a right-angled triangle, SOH-CAH-TOA: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent (= sin θ/cos θ). Learn the standard values: sin 30° = ½, cos 60° = ½, tan 45° = 1, sin 60° = cos 30° = √3/2, tan 60° = √3. The key ident…

How do I answer Trigonometry questions quickly in JAMB?

Read the stem carefully, eliminate clearly wrong options, and match the remaining choices to the key facts for Trigonometry. Practising timed Trigonometry questions builds the speed you need for UTME's pace of about 40 seconds per question.

Are these JAMB Mathematics Trigonometry questions past questions or original?

They are original questions written to JAMB (UTME) standard and mapped to the official syllabus — not reproduced past papers. This keeps them legal to use freely while closely mirroring how the real exam tests the topic.

Where can I practise Trigonometry questions free without signing up?

Right here — tap “Start Trigonometry practice” on this page to begin instantly. Belmadeng's CBT practice is completely free and needs no sign-up, download or subscription.

About these questions: original, JAMB-standard items written from the official UTME Mathematics syllabus (last reviewed 2026-09-18). Belmadeng is an independent study platform and is not affiliated with JAMB. Spotted an error? Use the report link.