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Compilation of Problems in Trigonometry


1. If sin A = 3/5 and A is in quadrant II while cos B = 7/25 and B is in quadrant I, find sin (A + B).

2. Solve for x in the equation: Arctan 2x + Arctan x = (π/2) - 45°.

3. If 84° - 0.4x = Arctan(cot0.25x). Find x.

4. Simplify: 4cosy siny (1 - 2sin2y)

5. Evaluate: cos [arctan 15/8 - arctan 7/24].

6. What is the measure in degrees of 2.25 revolutions counterclockwise?

7. Find the value of x in the equation cscx + cotx = 3.

8. If sec2A = 5/2, what is the quantity 1 - sin2A?

9. Of what quadrant is A, if sec A is positive and cscA is negative?

10. The angle of a sector is 30° and the radius is 15 cm. What is the area of the sector?

11. A man finds the angle of elevation of the top of the tower to be 30°. He walks 85 m nearer the tower and finds its angle of elevation to be 60°. What is the height of the tower?

12. Evaluate: Arctan[2 cos (arc sin(√3/2)]

13. Points A and B are 1000 m apart are plotted on a straight highway running east and west. From A, the bearing of tower C is N32°W and from B the bearing of C is N26°E. Approximate the shortest distance of the tower from the highway.

14. A rotating wheel has a radius of 2 feet and 6 inches. A point on the rim of the wheel moves 30 feet in 2 sec. Find the angular velocity of the wheel.

15. Solve for A:cos2A = 1 - cos2A

16. Evaluate:sin (270° - A)

17. If sec2 A = 5/2, find 1 – sin2A.

18. Simplify: (cosA)^4 - (sinA)^4

19. Assuming that the earth is a sphere whose radius is 6400 km. Find the distance along a 3°arc at the equator of the earth’s surface.

20. A central angle of 45° subtends an arc of 12 cm. What is the radius of the circle?

21. If tan 4A = cot 6A, then what is the value of angle A?

22. A railroad is to be laid-off in a circular path. What should be the radius if the track is to change direction by 30° at a distance of 157.08 m?

23. Solve for x: arctan x + arctan (1/3) = π/4.

24. You are given one coin with 5-cm diameter and a large supply of coins with diameter of 2 cm. What is the maximum number of the smaller coins that may be arranged tangentially around the larger without any overlap?

25. Determine the period of the curve y = sin (1/2) x.

26. Given: x = (cosB tanB – sinB)/cosB. Solve for x if B = 30°.

27. A flywheel of radius 14 inches is rotating at the rate of 1000 rpm. How fast does a point on the rim travels in ft/sec?

28. Solve angle A of an oblique triangle with vertices ABC, if a = 25, b = 16 and C = 94°6´.

29. If sin A = 2.5x and cos A = 5.5x, find the value of A.

30. Triangle ABC is a right triangle with right angle at C. CD is perpendicular to AB. BC = 4 and CD = 1. Find the area of the triangle ABC.

31. A ladder 5 m long leans against the wall of an apartment house forming an angle of 50° 32´with the ground. How high up the wall does it reach?

32. If cot 2Acot 68° = 1, then what is tan A?

33. Simplify the expression: sinB + cosB tanB/cosB.

34. If A is in the III quadrant and cos A = -15/17, find the value of cos (A/2).

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