Trigonometry for SSC CGL Cheat Sheet

Key Definitions

• Trigonometric Ratios: Ratios of the sides of a right triangle.

• Sine (sin): sin(θ) = Opposite/Hypotenuse

• Cosine (cos): cos(θ) = Adjacent/Hypotenuse

• Tangent (tan): tan(θ) = Opposite/Adjacent

Important Concepts

Trigonometric Functions

• Reciprocal Functions:

• csc(θ) = 1/sin(θ)

• sec(θ) = 1/cos(θ)

• cot(θ) = 1/tan(θ)

• Pythagorean Identity:

• sin²(θ) + cos²(θ) = 1 ✅

Angle Sum and Difference

• sin(α ± β) = sin(α)cos(β) ± cos(α)sin(β)

• cos(α ± β) = cos(α)cos(β) ∓ sin(α)sin(β)

Key Formulas

• Basic Trigonometric Ratios:

• sin(0°) = 0 ✅

• sin(30°) = 1/2 ✅

• sin(45°) = √2/2 ✅

• sin(60°) = √3/2 ✅

• sin(90°) = 1 ✅

• Sum of Angles:

• tan(α + β) = (tan(α) + tan(β)) / (1 - tan(α)tan(β))

Common Mistakes to Avoid

Common Mistake: Confusing sine and cosine values for angles (e.g., sin(90°) ≠ cos(0°))

Memory Tricks

Tip: "SOH CAH TOA" —

• Sine = Opposite/Hypotenuse

• Cosine = Adjacent/Hypotenuse

• Tangent = Opposite/Adjacent

Key Diagrams

         |\
         | \
  Opposite|  \ Hypotenuse
         |   \
         |____\
           Adjacent