Class 10 Maths - Trigonometry Notes
1. Trigonometric Ratios (of acute angles)
In a right-angled triangle:
- Perpendicular: Opposite side of the angle
- Base: Adjacent side of the angle
- Hypotenuse: Longest side (opposite the right angle)
Trigonometric Ratios:
- sin A = Perpendicular / Hypotenuse
- cos A = Base / Hypotenuse
- tan A = Perpendicular / Base
- cosec A = Hypotenuse / Perpendicular
- sec A = Hypotenuse / Base
- cot A = Base / Perpendicular
2. Reciprocal Identities
- sin A = 1 / cosec A
- cos A = 1 / sec A
- tan A = 1 / cot A
3. Trigonometric Ratios of Standard Angles
| Angle | sin | cos | tan | cosec | sec | cot |
|-------|---------|---------|-------|--------|-------|-------|
| 0° |0 |1 |0 | inf |1 | inf |
| 30° | 1/2 | sqrt(3)/2 | 1/sqrt(3) | 2 | 2/sqrt(3) | sqrt(3) |
| 45° | 1/sqrt(2) | 1/sqrt(2) | 1 | sqrt(2) | sqrt(2) | 1 |
| 60° | sqrt(3)/2 | 1/2 | sqrt(3) | 2/sqrt(3) | 2 | 1/sqrt(3) |
| 90° | 1 |0 | inf | 1 | inf | 0 |
4. Trigonometric Identities
1. Trigonometric Ratios (of acute angles)
In a right-angled triangle:
- Perpendicular: Opposite side of the angle
- Base: Adjacent side of the angle
- Hypotenuse: Longest side (opposite the right angle)
Trigonometric Ratios:
- sin A = Perpendicular / Hypotenuse
- cos A = Base / Hypotenuse
- tan A = Perpendicular / Base
- cosec A = Hypotenuse / Perpendicular
- sec A = Hypotenuse / Base
- cot A = Base / Perpendicular
2. Reciprocal Identities
- sin A = 1 / cosec A
- cos A = 1 / sec A
- tan A = 1 / cot A
3. Trigonometric Ratios of Standard Angles
| Angle | sin | cos | tan | cosec | sec | cot |
|-------|---------|---------|-------|--------|-------|-------|
| 0° |0 |1 |0 | inf |1 | inf |
| 30° | 1/2 | sqrt(3)/2 | 1/sqrt(3) | 2 | 2/sqrt(3) | sqrt(3) |
| 45° | 1/sqrt(2) | 1/sqrt(2) | 1 | sqrt(2) | sqrt(2) | 1 |
| 60° | sqrt(3)/2 | 1/2 | sqrt(3) | 2/sqrt(3) | 2 | 1/sqrt(3) |
| 90° | 1 |0 | inf | 1 | inf | 0 |
4. Trigonometric Identities
