RRB PREP
NTPC ALP Group D

Trigonometry for RRB Exams

Trigonometric Ratios

Right-Angled Triangle

In a right-angled triangle with angle θ:

  • • sin θ = Perpendicular / Hypotenuse (P/H)
  • • cos θ = Base / Hypotenuse (B/H)
  • • tan θ = Perpendicular / Base (P/B) = sin θ / cos θ
  • • cosec θ = 1 / sin θ = H/P
  • • sec θ = 1 / cos θ = H/B
  • • cot θ = 1 / tan θ = B/P

Pythagoras Theorem: H² = P² + B²

Standard Angles Table

θ 0° 30° 45° 60° 90°
sin θ 0 1/2 1/√2 √3/2 1
cos θ 1 √3/2 1/√2 1/2 0
tan θ 0 1/√3 1 √3 ∞

Trigonometric Identities

Square Identities

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

Complementary Angles

  • • sin(90°-θ) = cos θ
  • • cos(90°-θ) = sin θ
  • • tan(90°-θ) = cot θ
  • • cosec(90°-θ) = sec θ

Heights & Distances

Key Concepts

  • • Angle of Elevation: Angle above horizontal line when looking up
  • • Angle of Depression: Angle below horizontal line when looking down
  • • Tip: Always draw a diagram first. Use tan θ (P/B) most frequently.

Test Your Knowledge

30 random questions • 1 minute per question