Trigonometry
About 6 min · Quantitative Aptitude (Basic Arithmetic Skill) · English
Time worked out from the lesson's 352 words at 150 words a minute, plus a minute for each question.
Trigonometry in SSC CHSL tests your understanding of angular relationships in right triangles and their practical applications.
Key ideas
- Six trigonometric ratios exist for any acute angle θ in a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent, cot θ = adjacent/opposite, sec θ = hypotenuse/adjacent, csc θ = hypotenuse/opposite. These definitions are the foundation of all problems.
- Reciprocal identities link pairs of ratios: sin θ = 1/csc θ, cos θ = 1/sec θ, tan θ = 1/cot θ. Also, tan θ = sin θ / cos θ and cot θ = cos θ / sin θ. Use these to convert between ratios when needed.
- Pythagorean identities: sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, 1 + cot² θ = csc² θ. These let you find one ratio when another is given.
- Complementary angle identities apply when angles add to 90°: sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, tan(90° − θ) = cot θ. Useful for simplification in identities.
- Standard angle values (0°, 30°, 45°, 60°, 90°) must be memorized. For example, sin 30° = 1/2, cos 45° = 1/√2, tan 60° = √3, sin 90° = 1.
Quick reference
- Memorize the angle table: sin/cos/tan for 0°, 30°, 45°, 60°, 90° — non-negotiable for speed.
- Three Pythagorean identities: sin² + cos² = 1, 1 + tan² = sec², 1 + cot² = csc².
- Complementary swap: sin(90° − θ) = cos θ, tan(90° − θ) = cot θ.
- Heights-distances formula: tan(angle) = height / base distance — draw the triangle every time.
- Reciprocal pairs: sin ↔ csc, cos ↔ sec, tan ↔ cot.
Check yourself: 3 questions
1. If sin θ = 3/5 and θ is an acute angle, then what is the value of tan θ?
2. What is the value of (sin 30° + cos 60°) × (cos 45°)?
3. A person is standing 30 meters away from a building. The angle of elevation to the top of the building is 60°. What is the height of the building?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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