6.1

Trigonometric ratios

Cambridge IGCSE Mathematics (0580)  · Unit 6: Trigonometry  · 9 flashcards

Trigonometric ratios is topic 6.1 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 6 — Trigonometry , alongside Sine and cosine rules, 3D trigonometry and Trigonometric graphs.  In one line: Trigonometry is the branch of mathematics that studies the relationships between angles and sides of triangles, particularly right-angled triangles. It allows us to calculate unknown lengths or angles.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 9 flashcards — 4 definitions, 1 key concept and 2 application cards — covering the precise wording mark schemes reward.  Use the 4 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

'trigonometry'

Trigonometry is the branch of mathematics that studies the relationships between angles and sides of triangles, particularly right-angled triangles. It allows us to calculate unknown lengths or angles.

Example: if you know the angle of elevation to the top of a building is 30 degrees and you are standing 50 meters from the base, you can use trigonometry to find the height of the building.

Questions this Trigonometric ratios deck will help you answer

Definition Flip

Define 'trigonometry'.

Answer Flip

Trigonometry is the branch of mathematics that studies the relationships between angles and sides of triangles, particularly right-angled triangles. It allows us to calculate unknown lengths or angles.

Example: if you know the angle of elevation to the top of a building is 30 degrees and you are standing 50 meters from the base, you can use trigonometry to find the height of the building.
Definition Flip

In a right-angled triangle, what does 'SOH CAH TOA' stand for?

Answer Flip

SOH CAH TOA is a mnemonic for trigonometric ratios. SOH: Sin = Opposite/Hypotenuse. CAH: Cos = Adjacent/Hypotenuse. TOA: Tan = Opposite/Adjacent.

Example: if the opposite side is 3cm and the hypotenuse is 5cm, then sin(θ) = 3/5.
Key Concept Flip

In a right-angled triangle, angle θ is given. If the opposite side is 6 and the hypotenuse is 10, what is sin(θ)?

Answer Flip

sin(θ) = Opposite/Hypotenuse. Therefore, sin(θ) = 6/10 = 0.6

Definition Flip

Define the term 'adjacent' in the context of trigonometric ratios.

Answer Flip

The adjacent side is the side next to the given angle (θ) in a right-angled triangle, that is not the hypotenuse. It forms one of the rays of the angle.

Definition Flip

Explain the difference between 'angle of elevation' and 'angle of depression'.

Answer Flip

Angle of elevation is the angle from the horizontal upwards to a point of interest. Angle of depression is the angle from the horizontal downwards to a point of interest.

Key Concept Flip

A ladder leans against a wall. The angle of elevation from the ground to the top of the ladder is 60 degrees. What trig ratio relates the ladder's length and the wall's height?

Answer Flip

Sine (sin) relates the opposite (wall height) to the hypotenuse (ladder's length). sin(60) = wall height/ladder length.

Key Concept Flip

If cos(x) = 0.8 and the adjacent side is 8, what is the length of the hypotenuse?

Answer Flip

Since cos(x) = Adjacent/Hypotenuse, 0.8 = 8/Hypotenuse. Therefore, Hypotenuse = 8/0.8 = 10.

Key Concept Flip

When would you use the tangent ratio (tan)?

Answer Flip

You would use the tangent ratio (tan) when you know, or need to find, the lengths of the opposite and adjacent sides of a right-angled triangle relative to a given angle.

Key Concept Flip

A building casts a shadow of 20m when the angle of elevation of the sun is 30 degrees. How tall is the building?

Answer Flip

We can use tan(30) = height/20. Therefore height = 20 * tan(30) ≈ 11.55m.

Review the material

Read revision notes with definitions, equations, and exam tips.

Read Notes

Test yourself

Practice with MCQ questions to check your understanding.

Take Mathematics Quiz
5.4 Volume 6.2 Sine and cosine rules

Key Questions: Trigonometric ratios

Define 'trigonometry'.

Trigonometry is the branch of mathematics that studies the relationships between angles and sides of triangles, particularly right-angled triangles. It allows us to calculate unknown lengths or angles.

Example: if you know the angle of elevation to the top of a building is 30 degrees and you are standing 50 meters from the base, you can use trigonometry to find the height of the building.
In a right-angled triangle, what does 'SOH CAH TOA' stand for?

SOH CAH TOA is a mnemonic for trigonometric ratios. SOH: Sin = Opposite/Hypotenuse. CAH: Cos = Adjacent/Hypotenuse. TOA: Tan = Opposite/Adjacent.

Example: if the opposite side is 3cm and the hypotenuse is 5cm, then sin(θ) = 3/5.
Define the term 'adjacent' in the context of trigonometric ratios.

The adjacent side is the side next to the given angle (θ) in a right-angled triangle, that is not the hypotenuse. It forms one of the rays of the angle.

Explain the difference between 'angle of elevation' and 'angle of depression'.

Angle of elevation is the angle from the horizontal upwards to a point of interest. Angle of depression is the angle from the horizontal downwards to a point of interest.

More topics in Unit 6 — Trigonometry

Trigonometric ratios sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

6.2 Sine and cosine rules

9 flashcards
6.3 3D trigonometry

10 flashcards
6.4 Trigonometric graphs

9 flashcards

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

trigonometry sine cosine tangent sin cos tan opposite adjacent hypotenuse SOH CAH TOA right-angled triangle angle of elevation angle of depression

Key terms covered in this Trigonometric ratios deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

'trigonometry'
In a right-angled triangle, what does 'SOH CAH TOA' stand for
The term 'adjacent' in the context of trigonometric ratios
Explain the difference between 'angle of elevation' and 'angle of depression'

Related Mathematics guides

Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.

IGCSE Maths vs Additional Maths

Choosing between 0580 and 0606, and what each paper expects

Cambridge maths notation guide

Notation conventions Cambridge expects in your answers

How to study this Trigonometric ratios deck

Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.