Trigonometric Ratios Part 2 - Introduction to Trigonometry, CBSE, Class 10, Mathematics

Trigonometry is an important branch of mathematics that deals with the relationships between the angles and sides of triangles. It has various applications in fields such as physics, engineering, and architecture. In this document, we will discuss important questions related to trigonometric ratios in the context of the CBSE Class 10 Mathematics curriculum.

1. What is Trigonometry?
Trigonometry is the study of relationships between the angles and sides of triangles. It involves the use of trigonometric ratios such as sine, cosine, and tangent to solve problems related to angles and sides of triangles.

2. What are Trigonometric Ratios?
Trigonometric ratios are ratios of the lengths of two sides of a right-angled triangle. The three main trigonometric ratios are:

- Sine (sinθ): The ratio of the length of the side opposite to the angle θ to the length of the hypotenuse.
- Cosine (cosθ): The ratio of the length of the adjacent side to the angle θ to the length of the hypotenuse.
- Tangent (tanθ): The ratio of the length of the side opposite to the angle θ to the length of the adjacent side.

3. How to Find Trigonometric Ratios?
To find the trigonometric ratios of an angle in a right-angled triangle, divide the length of the corresponding side by the length of the hypotenuse. For example:

- sinθ = Opposite/Hypotenuse
- cosθ = Adjacent/Hypotenuse
- tanθ = Opposite/Adjacent

4. What are the Values of Trigonometric Ratios for Special Angles?
For special angles such as 0°, 30°, 45°, 60°, and 90°, the values of trigonometric ratios are as follows:

- sin0° = 0, cos0° = 1, tan0° = 0
- sin30° = 1/2, cos30° = √3/2, tan30° = √3/3
- sin45° = √2/2, cos45° = √2/2, tan45° = 1
- sin60° = √3/2, cos60° = 1/2, tan60° = √3
- sin90° = 1, cos90° = 0, tan90° = ∞

5. How to Use Trigonometric Ratios to Solve Problems?
Trigonometric ratios can be used to solve problems involving angles and sides of triangles. By knowing the value of one trigonometric ratio, we can find the values of other ratios using trigonometric identities. We can also use inverse trigonometric functions to find the angles when the ratios are given.

Conclusion:
Trigonometry and trigonometric ratios play a vital role in solving problems related to angles and sides of triangles. Understanding the concepts and properties of trigonometric ratios is essential for students studying mathematics in Class 10. By practicing and solving questions related to trigonometric ratios, students can enhance their problem-solving skills and excel