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Maths · Quantitative Aptitude

Trig & Number Series

The miscellaneous section tests basic trigonometry (height-distance, identities) and number-series pattern recognition. These are easy 2–3 marks if you have the standard values memorised — and number series is a regular feature of every Ba…
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Why it matters

SSC CGL gives 2-3 trigonometry questions in Tier-I and full theorem-based questions in Tier-II. Banking exams (IBPS, SBI, RBI) use number series in both Quant and Reasoning sections.
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Trigonometry — Basic Identities

Trigonometry studies the relations between sides and angles of a triangle.

Exam tipMemorise the standard-angle table thoroughly. Most exam trigonometry questions are direct substitutions into these values.
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Heights & Distances

Heights & Distances is the application of trigonometry to find unknown heights or distances using angles of elevation and depression.

Exam tipThe angle of depression from A to B equals the angle of elevation from B to A — they are alternate interior angles.
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Number Series

A number series is a sequence of numbers arranged according to a definite rule. The task is to find the next term, the missing term, or the wrong term.

Exam tipWhen stuck, try ÷ between consecutive terms — if all divisions give equal ratios, it's a GP. If first differences are constant it is an AP. Otherwise look at squares or cubes.
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Short Tricks

Standard-angle table — burn it into memory
Memorise sin & cos for 0°, 30°, 45°, 60°, 90°. sin: 0, 1/2, 1/√2, √3/2, 1. cos is the same values reversed. tan = sin/cos.
Convert everything to sin and cos
For any tricky identity, replace tan, cot, sec, cosec by their sin/cos equivalents and use sin²θ + cos²θ = 1. Most identities collapse in 2…
Angle of depression = angle of elevation
The angle of depression from A down to B equals the angle of elevation from B up to A. Use whichever side gives an easier triangle.
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Quick Revision Facts

  • sin0° = 0, sin30° = 1/2, sin45° = 1/√2, sin60° = √3/2, sin90° = 1.
  • tan0° = 0, tan45° = 1, tan90° is undefined (infinity).
  • Sum of n terms of an AP = (n/2) × (first + last) or (n/2)[2a + (n−1)d].
  • Sum of n terms of a GP = a(rⁿ−1)/(r−1), for r ≠ 1.
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Mathematics — Quantitative Aptitude
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