How to Solve Trigonometry Problems Step by Step
FAQs on Trigonometry Practice Paper with Answers
1. What is trigonometry and why is it important in mathematics?
Trigonometry is the branch of mathematics that studies relationships between angles and sides of triangles, especially right-angled triangles. Its importance lies in its applications across science, engineering, physics, navigation, and daily calculations, as it helps solve real-world problems involving heights, distances, and angles.
Key points:
- Deals with angles and side lengths in triangles
- Uses sine, cosine, and tangent ratios
- Foundational for many advanced mathematical concepts and exams
- Essential in fields like architecture, surveying, and physics
2. What are the six trigonometric ratios?
The six trigonometric ratios are mathematical relationships used to relate the angles and sides of a right-angled triangle. They are:
- Sine (sin θ) = Opposite / Hypotenuse
- Cosine (cos θ) = Adjacent / Hypotenuse
- Tangent (tan θ) = Opposite / Adjacent
- Cosecant (csc θ) = 1/sin θ = Hypotenuse / Opposite
- Secant (sec θ) = 1/cos θ = Hypotenuse / Adjacent
- Cotangent (cot θ) = 1/tan θ = Adjacent / Opposite
3. How do you remember the values of trigonometric ratios for standard angles?
Standard angle values in trigonometry (like 0°, 30°, 45°, 60°, 90°) can be easily remembered using simple patterns and tables.
Tips to remember:
- Memorise the standard angle table for sin, cos, and tan
- Use the 0-4 pattern under square roots for sin θ and reverse for cos θ
- For tan θ, divide sin θ by cos θ
4. What is the Pythagorean identity in trigonometry?
The Pythagorean identity is a fundamental trigonometric relationship stating that for any angle θ:
- sin²θ + cos²θ = 1
- Other forms: 1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ
5. How can trigonometry be applied to solve real-life problems?
Trigonometry is widely used to solve real-life problems that involve distances, heights, and angles.
Examples:
- Finding heights of towers and trees without directly measuring them
- Calculating distances between distant objects using angles of elevation or depression
- Navigation and construction to determine correct angles and measurements
- Used in engineering, physics, and geography projects
6. What is the formula for finding the area of a triangle using trigonometry?
The area of a triangle can be calculated using trigonometry when two sides and the included angle are known.
Formula:
- Area = ½ ab sin C
7. What do sine, cosine, and tangent represent in a right triangle?
In a right-angled triangle, sine, cosine, and tangent are ratios that compare the lengths of different sides.
- Sine (sin θ): Ratio of the length of the side opposite to angle θ to the hypotenuse
- Cosine (cos θ): Ratio of adjacent side to hypotenuse
- Tangent (tan θ): Ratio of opposite side to adjacent side
8. How do you solve trigonometric problems involving angles of elevation and depression?
Problems involving angles of elevation and depression require applying trigonometric ratios to real-world heights and distances.
- Draw clear diagrams showing positions and angles
- Use tan θ, sin θ, or cos θ as appropriate
- Arrange known and unknown values according to the question
- Solve for the unknown using algebraic steps
9. What are the applications of trigonometry in different fields?
Trigonometry has important applications in many disciplines beyond mathematics.
- Engineering: For design, measurement, and analysis of structures
- Physics: To study waves, oscillations, and forces
- Geography: In mapping and navigation
- Astronomy: For calculating distances between celestial bodies
10. Is it necessary to memorise all trigonometric formulas for the CBSE exam?
Memorising key trigonometric formulas is crucial for success in the CBSE exam.
- Frequently used formulas include trigonometric ratios, identities, and standard angle values
- Memory aids and practise help recall in the exam
- Understanding concepts along with memorisation allows accurate application






















