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JAMB Mathematics · Geometry/Trigonometry

Trigonometry: JAMB Mathematics Past Questions and Answers

What the JAMB syllabus covers in Trigonometry

Our summary: Sine, cosine and tangent, and using them for heights, bearings and triangle areas.

  • Trigonometrical ratios of angles
  • Angles of elevation and depression
  • Bearings
  • Areas and solutions of triangle
  • Graphs of sine and cosine
  • Sine and cosine formulae

Objectives

  • Calculate the sine, cosine and tangent of angles between −360∘≤θ≤360∘-360^\circ \le \theta \le 360^\circ
  • Apply these special angles, e.g. 30∘30^\circ, 45∘45^\circ, 60∘60^\circ, 75∘75^\circ, 90∘90^\circ, 105∘105^\circ, 135∘135^\circ to solve simple problems in trigonometry
  • Solve problems involving angles of elevation and depression
  • Solve problems involving bearings
  • Apply trigonometric formulae to find areas of triangles
  • Solve problems involving sine and cosine graphs

Syllabus content © The Joint Admissions and Matriculation Board (UTME).

JAMB Mathematics questions on Trigonometry

  1. JAMB 2025A bird flies from a tree P on a bearing of N60º E to a building, Q, a distance of 200 km. It then changes course and flies to another tree R on a bearing of…
  2. JAMB 2025Given that Cos A = 12/13 for 0 ≤ A ≤ 90º, find Tan A.
  3. JAMB 2025If cos = x y , find tan in terms of x and y
  4. JAMB 2024If tan = 8/15 , simplify Sin - Cos /Sin^2 - Sin
  5. JAMB 2024From the top of a building 10m high, the angle of elevation of a fruit on top of a tree 25m is 30º. Calculate the horizontal distance between the building and…
  6. JAMB 2023The angle of elevation and depression of the top and bottom of another building, measured from the top of a 24 m tall building, is 30° and 60°, respectively…
  7. JAMB 2023A boat sails 8 km north from P to Q and then sails 6 km west from Q to R. Calculate the bearing of R from P. Give your answer to the nearest degree.
  8. JAMB 2022If sin θ = - 3/5 and θ lies in the third quadrant, find cos θ
  9. JAMB 2022If sec ^2 θ + tan ^2 θ = 3, then the angle θ is equal to?
  10. JAMB 2021X is due east point of y on a coast. Z is another point on the coast but 6.0km due south of Y. If the distance ZX is 12km, calculate the bearing of Z from X
  11. JAMB 2020A surveyor walks 500m up a hill which slopes at an angle of 30 ^o . Calculate the vertical height through which he rises
  12. JAMB 2019Given 58° = p° , find p.
  13. JAMB 2019Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.
  14. JAMB 2019Evaluate 2 30 + 5 60/ 60 , leaving your answer in surd form.
  15. JAMB 2019The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the…
  16. JAMB 2019If 4 ^2 x - 3 = 0 , find the value of x, when 0° x 90°
  17. JAMB 2019If x = 4/5 , find 1 + ^2 x/ ^2 x - 1 .
  18. JAMB 2018Tanθ is positive and Sinθ is negative. In which quadrant does θ lies
  19. JAMB 2018A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room.
  20. JAMB 2018A man stands on a tree 150cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.
  21. JAMB 2018From a point R, 300m north of P, a man walks eastwards to a place; Q which is 600m from P. Find the bearing of P from Q correct to the nearest degree
  22. JAMB 2018Given that Sin (5 x − 28) ^o = Cos(3 x − 50) ^o , o < x < 90 ^o Find the value of x
  23. JAMB 2018From a point P, Q is 5km due West and R is12km due South of Q. Find the distance between P and R.
  24. JAMB 2017Evaluate ( 45º + 30º ) in surd form
  25. JAMB 2015Given that tan x = 2/3 , where 0o d" x d" 90o, Find the value of 2sinx.
  26. JAMB 2013In triangle PQR, q = 8 cm, r = 6 cm and cos P = 1/12 . Calculate the value of p.
  27. JAMB 2013If = 3/4 , find the value of + .
  28. JAMB 2013Find the length of a chord which subtends an angle of 90° at the centre of a circle whose radius is 8 cm.
  29. JAMB 2012If angle is 135o, evaluate cos
  30. JAMB 2012A man stands on a tree 150 cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.
  31. JAMB 2011In a right angled triangle, if tan = 3/4 . What is cos - sin ?
  32. JAMB 2010If cot = 8/15 , where is acute, find sin

Years with Trigonometry questions in DeeepSolve's question bank

From the past questions DeeepSolve holds, not a count of everything the exam body has set.

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