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Syllabus
📋 SSC CGL
Subject:Tier-I Examination Syllabus

Trigonometry & Height-Distances

Syllabus Unit: Quantitative Aptitude

Why it matters

Chapter overview

SSC CGL trigonometry is purely numeric application, never calculus — the six trig ratios, the Pythagorean identities, the standard-angle table and elevation/depression triangle setups together account for several guaranteed questions every Tier-I paper. This topic builds ratio-identity fluency, instant recall of standard angle values, the single-triangle skill of height-distance problems, and the fixed max/min formulas for trig expressions.

Tier-I Examination Syllabus Quantitative Aptitude 25% weightage
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Trig Ratios
1sin, cos, tanOpp/Hyp, Adj/Hyp, Opp/Adj
2cosec, sec, cotReciprocals of sin, cos, tan
3Pythagorean Identitiessin²θ+cos²θ=1 and derivatives
4Quotient Relationstanθ=sinθ/cosθ

1Trigonometric Ratios & Identities

The six trig ratios are just side-ratios of a right triangle; the three Pythagorean identities let you find any ratio from any one given ratio.

Learning Objectives

  • Define sin, cos, tan, cosec, sec, cot as ratios of a right triangle's opposite, adjacent and hypotenuse sides.
  • Apply the three Pythagorean identities: sin²θ+cos²θ=1, 1+tan²θ=sec²θ, 1+cot²θ=cosec²θ.
  • Convert between any two trig ratios given one, using identities without ever computing the angle itself.
  • Simplify trig expressions using reciprocal relations (cosecθ=1/sinθ, etc.) and quotient relations (tanθ=sinθ/cosθ).

Key Terms

Trigonometric RatioThe ratio of two sides of a right triangle relative to a chosen acute angle, e.g. sinθ = opposite/hypotenuse.
Pythagorean Identitysin²θ+cos²θ=1, true for every value of θ, with two further identities derivable by dividing through by sin²θ or cos²θ.
Reciprocal Ratioscosecθ = 1/sinθ, secθ = 1/cosθ, cotθ = 1/tanθ.
Quotient Relationtanθ = sinθ/cosθ and cotθ = cosθ/sinθ.

All of trigonometry starts from labelling a right triangle's sides relative to one acute angle θ: opposite, adjacent, and hypotenuse.

sinθ = Opp/Hyp cosθ = Adj/Hyp tanθ = Opp/Adj cosecθ = 1/sinθ secθ = 1/cosθ cotθ = 1/tanθ

The three Pythagorean identities

sin²θ + cos²θ = 1 1 + tan²θ = sec²θ 1 + cot²θ = cosec²θ

Given any one ratio, these identities recover every other ratio without needing the angle's actual value — e.g. from sinθ=3/5, cos²θ=1−9/25=16/25 gives cosθ=4/5 directly.

Common MistakeTrap: always check the quadrant/sign convention implied by the question (SSC height-distance problems use acute angles only, so all ratios stay positive) before taking a square root.