Trigonometry — IGCSE Mathematics (0580) questions by topic
Trigonometry questions here work backwards from a given area or angle of elevation to an unknown side or angle, such as finding an included angle from a triangle's area, calculating an elevation angle between two points on a right-angled structure, or solving a sine equation across a full 0 to 360 degree range. Calculate, find, draw, deduce and explain want the correct trig ratio chosen and applied to the labelled sides, not a formula picked at random.
33 questions from 2023 to 2025 sit on this page, worth between 2 and 17 marks. Because a single wrong side chosen as opposite or adjacent throws off an entire answer, submitting your working for instant marking flags that mismatch immediately, right where it happens, rather than only once a final angle turns out wrong.
May–June 2025, Paper 21
The diagram shows a right-angled triangle. The angle at the lower-left vertex is 30°, the horizontal base is x cm, the vertical right-hand side is 6 cm, and the right angle is at…
Answer this question and get it marked →May–June 2025, Paper 22
Write down the exact value of tan 60 degrees.
Answer this question and get it marked →May–June 2025, Paper 23
May–June 2025, Paper 31
The diagram shows a right-angled triangle ABC (NOT TO SCALE). The right angle is at B. AB = 52.5 cm (the vertical side) and AC = 59.5 cm (the hypotenuse). BC is the horizontal…
Answer this question and get it marked →The diagram shows a right-angled triangle PQR (NOT TO SCALE). The right angle is at Q. PQ = 6 cm (vertical side), PR = 8 cm (hypotenuse), with R at the bottom-right. The diagram…
Answer this question and get it marked →May–June 2025, Paper 32
The diagram shows two right-angled triangles. Triangle ABD has the right angle at D, AD = 10.8 m, AB = 14.7 m. Triangle BCD has the right angle at B, BC = d m, and angle BDC =…
Answer this question and get it marked →May–June 2025, Paper 33
The diagram shows a right-angled triangle (not to scale). The top side is 35 cm, the right-hand vertical side is 22 cm, and the hypotenuse (the sloping side from the top-left…
Answer this question and get it marked →The diagram shows a right-angled triangle (not to scale). The angle at the top vertex is 52°, the vertical right-hand side (adjacent to the 52° angle) is 18.4 cm, and the…
Answer this question and get it marked →May–June 2025, Paper 41
The diagram shows triangle PQR (not to scale). Angle QPR = 42° at P, angle PQR = 115° (the interior angle at Q), and PQ = 12.5 cm. R is the upper-right vertex. Calculate the…
Answer this question and get it marked →The diagram shows a quadrilateral ABCD. In triangle ABD, AB = 9.6 cm, BD = 12.1 cm and angle ABD = 56°. Calculate AD.
Answer this question and get it marked →The diagram shows a pyramid OABCD. The pyramid has a square base, ABCD, with sides 10.5 cm. The vertex O is vertically above the centre of the base, M. The height of the pyramid…
Answer this question and get it marked →May–June 2025, Paper 42
The diagram shows a quadrilateral ABCD. CD = 10 m and DB = 12 m. Angle DBA = 90°, angle CDB = 56° and angle ADB = 34°. Calculate the length of AB.
Answer this question and get it marked →The diagram shows a cube (not to scale). The base is ABCD and the top vertex above C is P; the cube has edges of equal length and AP is a space diagonal from base vertex A to the…
Answer this question and get it marked →May–June 2025, Paper 43
Sketch the graph of y = sin x for 0 degrees <= x <= 360 degrees. (Axes are provided with y from -1 to 1 and x from 0 to 360 degrees.)
Answer this question and get it marked →May–June 2023, Paper 11
The diagram shows a right-angled triangle with the side opposite y° equal to 7.5 cm and the side adjacent to y° equal to 12.8 cm. Calculate the value of y.
Answer this question and get it marked →May–June 2023, Paper 12
The diagram shows a right-angled triangle ABC with the right angle at B, AC = 8.6 cm and angle ACB = 42°. Calculate AB.
Answer this question and get it marked →May–June 2023, Paper 21
The diagram shows the position of three towns U, V and W. U is due west of V and angle UVW = 125°. UV = 27.3 km and VW = 62.4 km. Calculate the bearing of U from W.
Answer this question and get it marked →On the diagram, sketch the graph of y = cos x for 0° ⩽ x ⩽ 360°.
Answer this question and get it marked →May–June 2023, Paper 22
The diagram shows a triangle with two sides 92.5 cm and 71 cm and the included acute angle marked x°. The area of the triangle is 2143 cm². Work out the value of x.
Answer this question and get it marked →Solve the equation 5 sin x = −3 for 0° ⩽ x ⩽ 360°.
Answer this question and get it marked →May–June 2023, Paper 42
The diagram shows the straight roads between town A, town B and town C. AC = 60 km, CB = 87 km and B is due east of A. The bearing of C from A is 038°. NOT TO SCALE. Show that…
Answer this question and get it marked →ABCDEFGH is a cuboid with a square base of side x cm. CG = 20 cm and AG = 28 cm. NOT TO SCALE. Calculate the value of x.
Answer this question and get it marked →May–June 2023, Paper 43
ABC is a scalene triangle on horizontal ground. AYX is a straight vertical post, held in place by two straight wires XB and YC. AC = 4.8 m, BC = 5.6 m and angle ACB = 20.4°. NOT…
Answer this question and get it marked →October–November 2023, Paper 12
ABC is a right-angled triangle, with the right angle at B. BC = 18 cm and angle BCA = 34°. NOT TO SCALE. Calculate AC.
Answer this question and get it marked →October–November 2023, Paper 21
A triangle has a side of length 8.3 cm with an angle of 105° between it and a side of length 16.2 cm; y° is the angle opposite the 8.3 cm side. NOT TO SCALE. Calculate the value…
Answer this question and get it marked →Sketch the graph of y = cos x for 0° ≤ x ≤ 360°.
Answer this question and get it marked →October–November 2023, Paper 23
In triangle PQR, PQ = 18 cm, RQ = 13.5 cm and angle QPR = 42°. NOT TO SCALE. Calculate the obtuse angle PRQ.
Answer this question and get it marked →The diagram shows a cuboid ABCDEFGH. AB = 14 cm, BC = 5 cm and CG = 8 cm. M is the midpoint of HG. NOT TO SCALE. Calculate BM.
Answer this question and get it marked →October–November 2023, Paper 41
ACD is a right-angled triangle (right angle at A). B is on AC and BC = 54.5 m. AD = 83.2 m and angle ABD = 38°. NOT TO SCALE. Calculate angle ACD.
Answer this question and get it marked →October–November 2023, Paper 42
The diagram shows a right-angled triangle. The hypotenuse is (2t + 3) cm, one leg is t cm (opposite the angle w°) and the other leg is 5 cm. NOT TO SCALE. Find the value of w.
Answer this question and get it marked →The diagram shows a right-angled triangle PQR on horizontal ground. X is vertically above R and the angle of elevation of X from P is 21°. XR = 2.8 m and RQ = 7.1 m. NOT TO SCALE.…
Answer this question and get it marked →October–November 2023, Paper 43
Complete the table of values for y = 3 cos 2x°. Values given to 1 dp. x 0 10 20 30 40 45 50 60 70 80 90 --- --- --- --- --- --- --- --- --- --- --- --- y 3.0 2.8 2.3 1.5 0.5 −0.5…
Answer this question and get it marked →The diagram shows a shape made from a major sector AOB and triangles OBC and AOD. OB = 6 cm, BC = 2 cm, obtuse angle AOC = 135° and angle BCO = 90°. NOT TO SCALE. Show that angle…
Answer this question and get it marked →Other IGCSE Mathematics topics
- Number (230)
- Algebra and graphs (150)
- Geometry (93)
- Mensuration (54)
- Statistics (52)
- Transformations and vectors (32)
- Probability (27)
- Coordinate geometry (16)