Class 10 Maths Chapter 8: Introduction to Trigonometry Concept Infographic (NCERT)
Chapter 8: Introduction to Trigonometry
Mastering the mathematical magic of right-angled triangles and ratios.
📖 The 3 Pillars
The longest side, directly opposite the 90° angle.
The side facing directly opposite to the reference angle A.
The side adjacent (next to) the reference angle A.
sin A = P / H
cos A = B / H
tan A = P / B
📊 The Value Table
For specific standard angles (0° to 90°)
| ∠ A | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin A | 0 | 12 |
1√2 |
√32 |
1 |
| cos A | 1 | √32 |
1√2 |
12 |
0 |
| tan A | 0 | 1√3 |
1 | √3 | N.D. |
| cosec A | N.D. | 2 | √2 | 2√3 |
1 |
| sec A | 1 | 2√3 |
√2 | 2 | N.D. |
| cot A | N.D. | √3 | 1 | 1√3 |
0 |
📐 Core Identities
Derived directly from the Pythagoras Theorem.
sin²A + cos²A = 1
True for all 0° ≤ A ≤ 90°
1 + tan²A = sec²A
True for all 0° ≤ A < 90°
cot²A + 1 = cosec²A
True for all 0° < A ≤ 90°
⭐ Board Exam Super-Hacks
Maximum Value Check
Because the hypotenuse is the longest side, the value of sin A or cos A is NEVER greater than 1. (Always ≤ 1). Conversely, sec A and cosec A are always ≥ 1.
The Reciprocal Magic
If you know sin A, simply flip the fraction to get cosec A.
cosec A = 1 / sin A | sec A = 1 / cos A
⚠️ Common Exam Traps
Trap 1: The Notation Myth
sin A is a single mathematical symbol. It is NOT the product of "sin" and "A". Separating them makes them completely meaningless!
Trap 2: Squaring the Angle
Remember that (sin A)² is written correctly as sin²A. Writing it as sin A² is wrong because you are squaring the angle, not the trigonometric ratio!
