Trigonometry is a crucial part of the Class 10 mathematics curriculum, focusing on the relationships between angles and sides in right-angled triangles. To strengthen understanding, students are often encouraged to practice objective questions on trigonometry. These questions test both conceptual clarity and quick application of formulas. Multiple-choice questions (MCQs) not only help in exam preparation but also improve time management and logical thinking. For students preparing for board exams or competitive tests, mastering objective questions in trigonometry is essential for building a strong mathematical foundation.
Importance of Objective Questions in Class 10 Trigonometry
Objective questions are a powerful tool to assess a student’s grasp of trigonometric concepts. Since these questions usually have one correct answer among several options, they require careful analysis and precise calculations. Here’s why they are beneficial:
- Help reinforce key trigonometric identities and formulas
- Enhance speed and accuracy in solving problems
- Ideal for self-assessment and quick revision
- Familiarize students with exam-style question formats
For Class 10 students, objective questions are especially useful in practicing topics such as trigonometric ratios, complementary angles, and height and distance problems.
Topics Covered in Trigonometry for Class 10
Before diving into objective questions, it’s important to know the core areas of trigonometry taught in Class 10. These areas often serve as the basis for multiple-choice questions:
- Trigonometric ratios: sin, cos, tan, cosec, sec, and cot
- Trigonometric identities
- Values of trigonometric ratios at standard angles (0°, 30°, 45°, 60°, and 90°)
- Complementary angles
- Applications of trigonometry in real life, such as heights and distances
These topics form the foundation for objective questions that assess both theoretical understanding and application-based problem-solving.
Sample Objective Questions on Trigonometry for Class 10
Trigonometric Ratios and Identities
- Q1: What is the value of sin 30°?
A) 1/2 B) √3/2 C) √2/2 D) 1
Answer: A) 1/2 - Q2: Which of the following is equal to 1?
A) sin²θ + cos²θ B) tan²θ + 1 C) sec²θ – tan²θ D) All of these
Answer: D) All of these - Q3: If cos A = 3/5, then find sin A (A is acute).
A) 4/5 B) 3/4 C) 5/4 D) 1/2
Answer: A) 4/5 - Q4: cot A is the reciprocal of:
A) sin A B) tan A C) sec A D) cos A
Answer: B) tan A - Q5: Which identity is correct?
A) tan²θ = sec²θ – 1
B) cot²θ + 1 = cosec²θ
C) sin²θ + cos²θ = 1
D) All of the above
Answer: D) All of the above
Standard Angle Values
- Q6: What is the value of tan 45°?
A) 0 B) 1 C) √3 D) Undefined
Answer: B) 1 - Q7: sin 90° equals:
A) 0 B) 1 C) √2/2 D) √3/2
Answer: B) 1 - Q8: Which of the following is true?
A) sin 0° = 1 B) cos 90° = 1
C) tan 0° = 0 D) sec 90° = 0
Answer: C) tan 0° = 0 - Q9: What is the value of cosec 30°?
A) 2 B) 1/2 C) 1 D) √3/2
Answer: A) 2 - Q10: sec 60° is equal to:
A) 2 B) 1/2 C) 2/√3 D) 2/3
Answer: C) 2/√3
Complementary Angles
- Q11: sin (90° – A) =
A) tan A B) cos A C) cot A D) sec A
Answer: B) cos A - Q12: Which pair is always equal?
A) sin A and cos (90° – A)
B) tan A and cot A
C) sec A and cosec A
D) cot A and cos (90° – A)
Answer: A) sin A and cos (90° – A) - Q13: cos (90° – A) is equal to:
A) sin A B) cot A C) tan A D) sec A
Answer: A) sin A - Q14: tan (90° – A) =
A) cot A B) tan A C) sin A D) sec A
Answer: A) cot A - Q15: cosec (90° – A) equals:
A) sec A B) tan A C) cot A D) cos A
Answer: A) sec A
Heights and Distances
- Q16: A tower casts a shadow of 20 m when the angle of elevation of the sun is 45°. The height of the tower is:
A) 10 m B) 20 m C) 30 m D) 40 m
Answer: B) 20 m - Q17: A ladder makes an angle of 60° with the ground and reaches a wall 10 m high. The length of the ladder is:
A) 5 m B) 10 m C) 20 m D) 15 m
Answer: D) 15 m - Q18: If the angle of elevation of the top of a pole from a point on the ground is 30° and the height of the pole is 10 m, the distance of the point from the pole is:
A) 5√3 m B) 10√3 m C) 20 m D) 15 m
Answer: B) 10√3 m - Q19: If tan θ = 3/4, then the value of sin θ is:
A) 3/5 B) 4/5 C) 5/3 D) 3/7
Answer: A) 3/5 - Q20: A man observes the top of a building at an angle of elevation of 60°. If the height of the building is 30 m, how far is he from its base?
A) 15 m B) 30√3 m C) 30/√3 m D) 10 m
Answer: C) 30/√3 m
Tips for Practicing Trigonometry Objective Questions
To master objective questions on trigonometry, here are some effective tips:
- Memorize standard trigonometric values and identities
- Practice mental calculations to save time during exams
- Work on questions involving right triangles and diagrams
- Use elimination strategies to rule out incorrect options
- Regularly attempt mock tests and timed quizzes
Consistent practice of Class 10 trigonometry MCQs improves confidence and performance. It also prepares students for future mathematics topics that are built upon these concepts.
Objective questions on trigonometry for Class 10 are a vital part of exam preparation. They not only test students’ understanding but also help develop problem-solving speed and accuracy. By practicing a wide variety of multiple-choice questions, students become familiar with different types of problems and strategies to tackle them. Trigonometry, when learned with conceptual clarity and regular practice, becomes an enjoyable and scoring topic. Focusing on formulas, identities, and real-world applications ensures better results and deeper understanding for all Class 10 learners.