Trigonometry is a vital part of Class 10 Mathematics and plays a significant role in shaping students’ understanding of angles, triangles, and their relationships. Many students find trigonometry both fascinating and challenging due to its blend of geometry and algebra. To strengthen concepts and improve problem-solving abilities, extra questions in trigonometry are an excellent resource. These questions help students prepare better for exams by testing their knowledge from different angles, improving speed, and boosting confidence. Practicing a variety of trigonometry questions is essential for mastering this crucial mathematical topic.
Understanding the Importance of Extra Questions in Trigonometry
In Class 10, trigonometry is introduced with a focus on right-angled triangles. It includes concepts such as trigonometric ratios, identities, and heights and distances. Solving extra questions helps reinforce these concepts by encouraging students to apply formulas and theorems in a variety of scenarios.
Why Practice Extra Questions?
- To understand the application of trigonometric ratios like sine, cosine, and tangent
- To gain familiarity with trigonometric identities and their simplification
- To improve problem-solving techniques for height and distance-based questions
- To prepare for board exams with a strong foundation
- To build speed and accuracy in mathematical reasoning
Key Concepts in Class 10 Trigonometry
Before jumping into extra questions, students must revise the following basic topics:
- Trigonometric Ratios: sin θ, cos θ, tan θ, cosec θ, sec θ, cot θ
- Trigonometric Identities: For example, sin²θ + cos²θ = 1
- Values of Trigonometric Ratios at Standard Angles: 0°, 30°, 45°, 60°, 90°
- Applications of Trigonometry: Finding heights and distances using angle of elevation and depression
Types of Extra Questions for Class 10 Trigonometry
Extra questions can be divided into different categories based on difficulty level and the specific concepts they focus on. Here’s how they can be categorized:
Basic-Level Questions
These questions focus on recalling definitions and evaluating basic trigonometric ratios.
- Find the value of sin 30° + cos 60°
- If tan A = 1, find angle A
- Evaluate: sin²45° + cos²45°
Intermediate-Level Questions
These involve applying identities and solving more complex expressions.
- If sin A = 3/5, find cos A and tan A
- Prove that: (1 + tan²A)/(1 + cot²A) = tan²A
- Evaluate: (1 + cos²30° – sin²60°)/(cot²45° + tan²0°)
Application-Based Questions
Application problems are word problems that test a student’s understanding of trigonometric use in real-life situations.
- A tower stands vertically on the ground. From a point on the ground 30 m away from the foot of the tower, the angle of elevation of the top of the tower is 60°. Find the height of the tower.
- A kite is flying at a height of 60 m attached to a string. If the angle between the string and the ground is 30°, find the length of the string.
- The angle of depression of a car from the top of a building is 45°. If the height of the building is 20 m, how far is the car from the base of the building?
Tips to Solve Trigonometry Extra Questions
To make the most out of extra practice questions, students should follow specific strategies that enhance accuracy and understanding.
1. Memorize Trigonometric Ratios
Be sure to memorize the standard trigonometric ratios and values. Use mnemonics like Some People Have Curly Brown Hair (for sin, cos, tan) to help remember the values easily.
2. Practice Identity Proofs
Trigonometric identities often appear in exams. Practice proving them step-by-step without skipping lines to avoid careless mistakes.
3. Draw Diagrams
When working with height and distance problems, always draw a right triangle based on the information given. Label all known and unknown sides and angles clearly.
4. Show All Steps
While solving, show all intermediate steps. Even if your final answer is wrong, partial steps can still earn marks.
5. Use Tables
Use trigonometric tables to quickly find values of sin, cos, and tan for standard angles if calculators are not allowed.
Common Mistakes to Avoid
Even well-prepared students make common errors when solving trigonometry problems. Being aware of these can help prevent them.
- Confusing between sin and cos values
- Incorrect simplification of identities
- Using wrong angles in height and distance problems
- Not converting degrees to radians if needed (in advanced cases)
- Overlooking the use of the correct unit (meters, degrees, etc.)
Sample Practice Set
Section A: Objective Type Questions
- sin 90° = ?
- cos 0° = ?
- tan 45° = ?
Section B: Short Answer Questions
- If cot A = 5/12, find sin A and cos A
- Prove that: 1 + tan²θ = sec²θ
- Evaluate: sin 60° à cos 30° + sin 30° à cos 60°
Section C: Long Answer Questions
- A man standing on the deck of a ship is 10 m above the water level. He observes the angle of elevation of the top of a lighthouse as 60° and the angle of depression of the base as 30°. Find the height of the lighthouse.
- From a point 40 m away from a building, the angle of elevation of the top of the building is found to be 60°. Find the height of the building.
Trigonometry in Class 10 is not just a set of formulas to memorize it is a powerful mathematical tool with real-life applications. Practicing extra questions sharpens your understanding, helps in mastering identities, and prepares you for exams more effectively. Whether solving simple ratio problems or complex height and distance situations, consistent practice with a variety of questions enhances both your skills and confidence. The more questions you solve, the more intuitive trigonometry becomes. Make it a habit to review formulas, solve extra questions regularly, and assess your progress through mock tests to score high in the Class 10 board exams.