Introduction
Trigonometry in SSC exams stays within a narrow, predictable band — the six ratios, the standard angle
table, and a handful of identities. Master these, and Height & Distance (next chapter) becomes
straightforward.
The Six Trigonometric Ratios (Right Triangle)
| Ratio | Formula |
|---|
| sin θ | Opposite / Hypotenuse |
| cos θ | Adjacent / Hypotenuse |
| tan θ | Opposite / Adjacent = sin θ / cos θ |
| cosec θ | 1 / sin θ |
| sec θ | 1 / cos θ |
| cot θ | 1 / tan θ |
Standard Angle Value Table — Memorise This
| θ | 0° | 30° | 45° | 60° | 90° |
|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | Undefined |
💡 Memory Trick: For sin, write 0,1,2,3,4 under a root and divide by 2 → √0/2, √1/2, √2/2, √3/2, √4/2 = 0, ½, 1/√2, √3/2, 1 — instantly gives all five sin values in order. Reverse the list for cos.
Key Trigonometric Identities
| Identity |
|---|
| sin²θ + cos²θ = 1 |
| 1 + tan²θ = sec²θ |
| 1 + cot²θ = cosec²θ |
Q. If sin θ = 3/5, find cos θ and tan θ (θ is acute).
Using the 3-4-5 Pythagorean triplet: opposite=3, hypotenuse=5, adjacent=4
cos θ = 4/5, tan θ = 3/4
Q. Evaluate: sin30° × cos60° + cos30° × sin60°
= (1/2)(1/2) + (√3/2)(√3/2) = 1/4 + 3/4 = 1 (this is actually sin(30+60) = sin90° = 1, confirming the compound angle rule)
Complementary Angle Relationships
| Relation |
|---|
| sin(90°−θ) = cos θ |
| tan(90°−θ) = cot θ |
| sec(90°−θ) = cosec θ |
Q. Evaluate: tan10° × tan20° × tan70° × tan80°
tan70° = cot20°, tan80° = cot10° (complementary pairs)
= tan10°×cot10° × tan20°×cot20° = 1 × 1 = 1
✅ Practice Focus: Six ratios and their reciprocal relationships · Standard angle table (0°,30°,45°,60°,90°) memorised via the √n/2 trick · Three Pythagorean identities · Complementary angle conversion for simplification.