Leaving Cert Maths: Trigonometry
How often Trigonometry comes up on the Maths papers, every year it was asked, and questions to try.
HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
OL Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
FL Asked on 5 of the last 7 Foundation Level papers, most recently in 2026. most years
Quick ones on Trigonometry.
- √3/2
- ½
- 1/√2
- 90°
- 360°
- 180°
- 1
- 2
- 0
Show the answers
(a) ½
(b) 180°
(c) 1
Higher Level
Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Paper 2, Q6, Paper 2, Q7, Paper 2, Q8, Paper 2, Q9 |
| 2025 | Paper 2, Q6, Paper 2, Q7, Paper 2, Q8 |
| 2024 | Paper 1, Q8, Paper 2, Q3, Paper 2, Q10 |
| 2023 | Paper 2, Q2, Paper 2, Q7, Paper 2, Q9 |
| 2022 | Paper 1, Q8, Paper 2, Q4, Paper 2, Q9 |
| 2021 | Paper 1, Q7, Paper 1, Q10, Paper 2, Q4, Paper 2, Q7, Paper 2, Q9 |
| 2019 | Paper 1, Q8, Paper 2, Q4, Paper 2, Q7, Paper 2, Q9 |
| 2018 | Paper 2, Q4, Paper 2, Q9 |
| 2017 | Paper 1, Q9, Paper 2, Q6, Paper 2, Q9 |
| 2016 | Paper 2, Q3, Paper 2, Q7, Paper 2, Q8 |
Links open the State Examinations Commission’s paper for that year.
More Trigonometry questions
Trigonometry, 2 marks
Area of a triangle using two sides and the included angle?
- ab sin C
- ½ab cos C
- ½ab sin C
Show the answer
½ab sin C
The height of the triangle is b sin C, so area = ½ × base × height = ½ab sin C. It's in the tables.
Trigonometry, 2 marks
Period of y = sin x, in degrees?
- 90°
- 360°
- 180°
Show the answer
360°
sin x repeats every full turn: sin (x + 360°) = sin x.
Trigonometry, 2 marks
tan A = ?
- sin A / cos A
- cos A / sin A
- 1 / sin A
Show the answer
sin A / cos A
tan = opposite/adjacent; dividing sin (opp/hyp) by cos (adj/hyp) gives the same thing.
Ordinary Level
Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q4, Q8 |
| 2025 | Q2, Q10 |
| 2024 | Q8, Q9 |
| 2023 | Q7, Q10 |
| 2022 | Q5, Q8, Q9 |
| 2021 | Q8, Q9 |
| 2019 | Q6, Q9 |
| 2018 | Q8 |
| 2017 | Q3, Q6 |
| 2016 | Q2, Q9 |
Links open the State Examinations Commission’s paper for that year.
More Trigonometry questions
Trigonometry, 2 marks
In a right-angled triangle, sin A = ?
- adjacent/hypotenuse
- opposite/adjacent
- opposite/hypotenuse
Show the answer
opposite/hypotenuse
SOH: sine is opposite over hypotenuse. CAH is cosine and TOA is tangent.
Trigonometry, 2 marks
A right-angled triangle has sides 3 and 4 beside the right angle. Find the hypotenuse.
- 25
- 5
- 7
Show the answer
5
Pythagoras: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5.
Trigonometry, 2 marks
In a right-angled triangle, cos A = ?
- adjacent/hypotenuse
- opposite/hypotenuse
- adjacent/opposite
Show the answer
adjacent/hypotenuse
CAH: cosine is adjacent over hypotenuse.
Foundation Level
Asked on 5 of the last 7 Foundation Level papers, most recently in 2026. most years
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q8 |
| 2025 | Not asked |
| 2024 | Q11 |
| 2023 | Q2 |
| 2022 | Q7 |
| 2021 | Q6 |
| 2019 | Not asked |
Links open the State Examinations Commission’s paper for that year.
More Trigonometry questions
Trigonometry, 2 marks
In a right-angled triangle, tan A = …
- adjacent ÷ opposite
- opposite ÷ hypotenuse
- opposite ÷ adjacent
Show the answer
opposite ÷ adjacent
tan A = opposite ÷ adjacent. The opposite side is across from angle A; the adjacent side is beside it.
Trigonometry, 2 marks
In a right-angled triangle, the longest side is called the …
- opposite
- hypotenuse
- adjacent
Show the answer
hypotenuse
The hypotenuse is the longest side. It is always across from the right angle.
Trigonometry, 2 marks
In a right-angled triangle, sin A = …
- opposite ÷ hypotenuse
- adjacent ÷ hypotenuse
- opposite ÷ adjacent
Show the answer
opposite ÷ hypotenuse
sin A = opposite ÷ hypotenuse. The hypotenuse is the longest side, across from the right angle.