Pariksha SaathiQuantitative Aptitude
Trigonometry: Practice Questions with Answers
20 practice questions on Trigonometry, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
Read the lesson on this topic →
-
Q.1
Simplify: (1 − cos²θ)(1 + cot²θ)
Show answer
Answer: 1
Solution:
- 1 − cos²θ = sin²θ, from the core identity.
- 1 + cot²θ = cosec²θ = 1/sin²θ, from the derived identity.
- Multiplying: sin²θ × (1/sin²θ) = 1.
-
Q.2
If sin θ = 3/5 and θ is acute, find cos θ.
Show answer
Answer: 4/5
Solution:
- Using sin²θ + cos²θ = 1: cos²θ = 1 − (3/5)² = 1 − 9/25 = 16/25.
- cos θ = √(16/25) = 4/5 (positive, since θ is acute).
-
Q.3
Evaluate: (sin 30° + cos 60°) / (1 + tan 45°)
Show answer
Answer: 1/2
Solution:
- sin 30° = 1/2 and cos 60° = 1/2, so the numerator = 1/2 + 1/2 = 1.
- tan 45° = 1, so the denominator = 1 + 1 = 2.
- Result = 1/2.
-
Q.4
If cos θ = 5/13 and θ is acute, find sec θ and cosec θ.
Show answer
Answer: sec θ = 13/5, cosec θ = 13/12
Solution:
- cos θ = 5/13 corresponds to a 5-12-13 right triangle, so sin θ = 12/13.
- sec θ = 1/cos θ = 13/5.
- cosec θ = 1/sin θ = 13/12.
-
Q.5
Evaluate: sin 35° / cos 55°
Show answer
Answer: 1
Solution:
- cos 55° = cos(90° − 35°) = sin 35°, using the complementary angle relationship.
- So the expression becomes sin 35° / sin 35° = 1.
-
Q.6
If tan θ = 3/4 and θ is acute, find sec θ.
Show answer
Answer: 5/4
Solution:
- Using 1 + tan²θ = sec²θ: sec²θ = 1 + (3/4)² = 1 + 9/16 = 25/16.
- sec θ = √(25/16) = 5/4.
-
Q.7
Evaluate: 2 sin²45° + 3 cos²45°
Show answer
Answer: 2.5
Solution:
- sin 45° = cos 45° = 1/√2, so sin²45° = cos²45° = 1/2.
- 2(1/2) + 3(1/2) = 1 + 1.5 = 2.5.
-
Q.8
Evaluate: tan 20° / cot 70°
-
Q.9
Simplify: (1 + tan²θ) × cos²θ
-
Q.10
If sin θ = 7/25 and θ is acute, find cosec θ and cos θ.
-
Q.11
If sin θ = 5/13 and θ is acute, find cos θ.
-
Q.12
Evaluate: sin 90° + cos 0° − sin 0°
-
Q.13
Evaluate: 3 sin²60° + 2 cos²30°
-
Q.14
If tan θ = 5/12 and θ is acute, find sec θ.
-
Q.15
For an acute angle θ, sinθ = 10/11. Find cosecθ.
- A 10/11
- B 1/11
- C -1.1
- D 1.1
Show answer
Correct answer: (D) 1.1
cosecθ is the reciprocal of sinθ. Therefore cosecθ = 1/(10/11) = 1.1. Check: multiplying 1.1 by 10/11 gives 1; positivity follows from the acute-angle condition.
-
Q.16
For an acute angle θ, sinθ = 4/5. Find cosecθ.
- A 1.25
- B 0.8
- C 0.2
- D -1.25
Show answer
Correct answer: (A) 1.25
cosecθ is the reciprocal of sinθ. Therefore cosecθ = 1/(4/5) = 1.25. Check: multiplying 1.25 by 4/5 gives 1; positivity follows from the acute-angle condition.
-
Q.17
For an acute angle θ, tanθ = 3/4. Find cotθ.
- A 4/3
- B 0.75
- C 0.25
- D -4/3
Show answer
Correct answer: (A) 4/3
cotθ is the reciprocal of tanθ. Therefore cotθ = 1/(3/4) = 4/3. Check: multiplying 4/3 by 3/4 gives 1; positivity follows from the acute-angle condition.
-
Q.18
For an acute angle θ, tanθ = 6/7. Find cotθ.
- A 6/7
- B 1/7
- C 7/6
- D -7/6
Show answer
Correct answer: (C) 7/6
cotθ is the reciprocal of tanθ. Therefore cotθ = 1/(6/7) = 7/6. Check: multiplying 7/6 by 6/7 gives 1; positivity follows from the acute-angle condition.
-
Q.19
For an acute angle θ, sinθ = 7/8. Find cosecθ.
- A 0.875
- B 0.125
- C 8/7
- D -8/7
Show answer
Correct answer: (C) 8/7
cosecθ is the reciprocal of sinθ. Therefore cosecθ = 1/(7/8) = 8/7. Check: multiplying 8/7 by 7/8 gives 1; positivity follows from the acute-angle condition.
-
Q.20
For an acute angle θ, tanθ = 9/10. Find cotθ.
- A 0.9
- B 0.1
- C -10/9
- D 10/9
Show answer
Correct answer: (D) 10/9
cotθ is the reciprocal of tanθ. Therefore cotθ = 1/(9/10) = 10/9. Check: multiplying 10/9 by 9/10 gives 1; positivity follows from the acute-angle condition.
How these questions were made
Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-03.
Authored by an AI assistant (ChatGPT) - not reviewed by a subject-matter expert.