Trigonometry — Study Notes for SSC MTS
Overview
Trigonometry in SSC MTS is limited but high-scoring. You'll face 1–2 questions testing trigonometric ratios (sin, cos, tan and their reciprocals) and a handful of fundamental identities. The exam does **not** expect height-distance problems or advanced angle transformations — focus entirely on ratio definitions, complementary angle relations, and the three Pythagorean identities.
Most questions are direct substitutions: given one ratio, find another; or simplify an expression using identities. A strong grasp of the six basic ratios for standard angles (0°, 30°, 45°, 60°, 90°) and comfort with algebraic manipulation of the three main identities will fetch you full marks. This topic connects to algebra (identities are equations) and mensuration (right triangles), so mastery here reinforces other chapters.
**Exam weight:** 1–2 questions out of 25 in Numerical Ability. Every mark counts in a competitive exam, and trigonometry questions are faster to solve than multi-step arithmetic once you memorize the essentials.
Key Concepts
• **Trigonometric ratios in a right triangle:** For an acute angle θ in a right triangle, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. The reciprocals are cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.
• **Standard angles:** Memorize exact values for 0°, 30°, 45°, 60° and 90°. For example, sin 30° = 1/2, cos 45° = 1/√2, tan 60° = √3. These appear in nearly every trigonometry question.
• **Pythagorean identities:** The three must-know identities are sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ. These let you convert one ratio into another or simplify complex expressions.
• **Complementary angle relations:** sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, tan(90° − θ) = cot θ, and their reciprocals follow the same swap. Use these when an angle like 60° and 30° appear together (since 60° + 30° = 90°).
• **Reciprocal relationships:** cosec θ and sin θ are reciprocals, as are sec θ and cos θ, and cot θ and tan θ. If you know one, the other is immediate: sec θ = 1/cos θ, so if cos θ = 3/5 then sec θ = 5/3.
• **Ratio interconversions:** tan θ = sin θ/cos θ and cot θ = cos θ/sin θ. These are handy when simplifying fractions involving multiple ratios.
Formulas / Key Facts
**Trigonometric Ratios (right triangle with angle θ):**
- sin θ = perpendicular / hypotenuse
- cos θ = base / hypotenuse
- tan θ = perpendicular / base
- cosec θ = hypotenuse / perpendicular = 1/sin θ
- sec θ = hypotenuse / base = 1/cos θ
- cot θ = base / perpendicular = 1/tan θ
**Standard Angle Values (memorize this table):** | Angle | 0° | 30° | 45° | 60° | 90° | |-------|-----|------|-------|------|------| | sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | | cos | 1 | √3/2| 1/√2 | 1/2 | 0 | | tan | 0 | 1/√3| 1 | √3 | undefined |