Trigonometry: past paper questions

Real questions on trigonometry

The newest 20 of 59 written questions. Open one to see it on the real paper.

1. 0580/21 · May/June 2026 · Q18[2]
   18 $y=\sin 60^{\circ }\times \tan 30^{\circ }$. Find the value of $y$. $y=$See it on the paper →
2. 0580/21 · May/June 2026 · Q21d[2]
   [Diagram: A cuboid $ABCDEFGH$ with $BF=2$ cm, $BC=6$ cm and $CD=9$ cm. A dotted line connects $E$ to $C$.] The diagram shows a solid cuboid $ABCDEFGH$. $BF=2$ cm, $BC=6$ cm and $CD=9$ cm. (d) The angle between $CE$ and the base $CDHG$ is $x^{\circ }$. Find the value of $\sin x^{\circ }$.See it on the paper →
3. 0580/22 · May/June 2026 · Q8[2]
   \begin{array}{ccccc} \frac{1}{\sqrt{3}} & \frac{1}{2} & \frac{1}{\sqrt{2}} & \sqrt{3} & \frac{\sqrt{3}}{2} \end{array} Complete these statements using values from the list. $\cos 45^{\circ }=$ ………………… $\tan 60^{\circ }=$ …………………See it on the paper →
4. 0580/23 · May/June 2026 · Q19[4]
   19 [Diagram: A right-angled triangle with the right angle at the bottom right. The bottom horizontal side is labelled $9\text{ cm}$. The vertical side on the right is labelled $x\text{ cm}$. The angle at the top vertex is $60^{\circ }$. The text "NOT TO SCALE" is shown above the diagram.] Find the exact value of $x$....See it on the paper →
5. 0580/42 · May/June 2026 · Q11[2]
   11 [Diagram: A right-angled triangle $WXY$ with the right angle at $X$. The side $WX$ is horizontal with length $12.4\text{ cm}$. The angle $\angle XWY$ is $29^{\circ }$. The side $XY$ is vertical. The text "NOT TO SCALE" is present.] Calculate $XY$.See it on the paper →
6. 0580/42 · May/June 2026 · Q14[2]

   2-mark question — its maths and diagrams are best seen on the paper.

   See it on the paper →
7. 0580/42 · May/June 2026 · Q16d[2]
   ABCDE is a square-based pyramid. EC and BD intersect at F. AF is perpendicular to the base BCDE. BC = 16.5 cm and AF = 28 cm. [Diagram: A square-based pyramid ABCDE with apex A and base BCDE. The base is a square with vertices B, C, D, E in order. The diagonals EC and BD intersect at F. A vertical dotted line AF conn...See it on the paper →
8. 0580/42 · May/June 2026 · Q18a[1]
   18 In this question, all lengths are in centimetres. [Diagram: Triangle ABC with side AC labelled $x$, side BC labelled $2x$, and angle ACB labelled $30^{\circ }$. Triangle DEF with right angle at E, side DE labelled $(x-4)$, side EF labelled $(2x-6)$. NOT TO SCALE] (a) Show that the area of triangle $ABC$ is $\frac{1}{2}...See it on the paper →
9. 0580/43 · May/June 2026 · Q7a[3]
   [Diagram: A right-angled triangle with vertices $A$, $B$, and an unlabeled right-angle vertex. The hypotenuse $AB$ is labeled $25\text{ m}$. The horizontal base is labeled $22\text{ m}$. The vertical side is labeled $h\text{ m}$. The right angle is at the bottom right corner. The text "NOT TO SCALE" is present.] The po...See it on the paper →
10. 0580/43 · May/June 2026 · Q7b[2]
    [Diagram: A right-angled triangle with vertices $A$, $B$, and an unnamed right-angle vertex. The hypotenuse $AB$ is labelled $25\text{ m}$. The horizontal base is labelled $22\text{ m}$. The vertical side is labelled $h\text{ m}$. The angle at the base of the vertical side is a right angle. The text "NOT TO SCALE" is p...See it on the paper →
11. 0580/43 · May/June 2026 · Q8b(ii)[2]
    AB and CD are parallel lines. AD and BC are straight lines that intersect at X. Angle ABX = $y^{\circ }$. (b) Triangle ABX is similar to triangle DCX. CX = 5 cm, XD = 8 cm and AD = 20 cm. (ii) Angle CXD = $80.5^{\circ }$. Work out the area of triangle CXD.See it on the paper →
12. 0580/43 · May/June 2026 · Q12a[2]

    2-mark “Sketch” question — its maths and diagrams are best seen on the paper.

    See it on the paper →
13. 0580/43 · May/June 2026 · Q12b[3]
    (b) Solve the equation $3\cos x+1=0$ for $0^{\circ }⩽x⩽360^{\circ }$.See it on the paper →
14. 0580/42 · February/March 2026 · Q20b[4]
    [Diagram: A quadrilateral $ABCD$ with diagonal $AC$. $AD=290\text{ m}$, $AC=450\text{ m}$, $AB=600\text{ m}$. Angle $ACD=34^{\circ }$, Angle $CAB=57^{\circ }$. Label "NOT TO SCALE".] The diagram shows points $A$, $B$, $C$ and $D$ on horizontal ground. (b) Show that angle $CAD=85.8^{\circ }$, correct to 1 decimal pl...See it on the paper →
15. 0580/42 · February/March 2026 · Q23[4]
    23 Two angles, $A$ and $B$, are formed when two lines meet at a point. Angle $A$ is given by the equation $2+3\tan A=-0.5$. Find the **two** possible values of angle $B$.See it on the paper →
16. 0580/02 · Specimen 2025 · Q22[4]

    4-mark question — its maths and diagrams are best seen on the paper.

    See it on the paper →
17. 0580/04 · Specimen 2025 · Q13a[2]

    2-mark “Calculate” question — its maths and diagrams are best seen on the paper.

    See it on the paper →
18. 0580/04 · Specimen 2025 · Q17[2]

    2-mark “Calculate” question — its maths and diagrams are best seen on the paper.

    See it on the paper →
19. 0580/22 · October/November 2025 · Q21a[2]

    2-mark question — its maths and diagrams are best seen on the paper.

    See it on the paper →
20. 0580/22 · October/November 2025 · Q21b[3]
    (b) Solve the equation $2\cos x+\sqrt{3}=0$ for $0^{\circ }⩽x⩽360^{\circ }$.See it on the paper →

What examiners said

Comprehensive responses • Most candidates were able to apply the sine rule using the correct angles and sides. • Many candidates then correctly found the required angle CAD, to greater accuracy than 1 decimal place, which was required in this ‘show that’ question. Limited responses • Many candidates did not keep a value to at least 4 significant figures throughout their working and rounded angle...

— Examiner report, February/March 2026, 0580/42 Q20(b) (Cambridge)

Comprehensive responses • A few candidates gave a fully correct answer with correct working. • Some candidates solved the equation correctly to give A = –39.8° followed by at least one correct value of A in the range 0° to 360°. The values of B were often then calculated correctly. • Those candidates who sketched the tan graph or drew other trigonometrical diagrams were most successful in finding...

— Examiner report, February/March 2026, 0580/42 Q23 (Cambridge)

The most common error was to answer 1; other values given were , , and . 2 2 3 2

— Examiner report, May/June 2025, 0580/23 Q23(a) (Cambridge)