Lesson 4.2: Trigonometry (Heights, Distances, Identities)

Trigonometry is an important part of the Mathematics section for NDA, CDS, and AFCAT exams. It helps aspirants solve problems related to angles, heights, distances, and trigonometric identities, which frequently appear in competitive exams.

1. Basics of Trigonometry

• Trigonometric Ratios:

  • sin θ = Opposite / Hypotenuse

  • cos θ = Adjacent / Hypotenuse

  • tan θ = Opposite / Adjacent

  • cot θ = 1 / tan θ, sec θ = 1 / cos θ, cosec θ = 1 / sin θ

• Important Identities:

  • sin²θ + cos²θ = 1

  • 1 + tan²θ = sec²θ

  • 1 + cot²θ = cosec²θ

  • sin 2θ = 2 sin θ cos θ

  • cos 2θ = cos²θ – sin²θ

2. Heights and Distances

• Concept: Use trigonometric ratios to find heights of objects and distances.

• Common Problems:

  • Height of a tower, distance of a ship from a lighthouse

  • Angle of elevation and angle of depression problems

• Formula Examples:

  • Height = Distance × tan(Angle of Elevation)

  • Distance = Height / tan(Angle of Elevation)

3. Solving Trigonometry Problems

1. Identify angle of elevation/depression or given sides.

2. Apply basic trigonometric ratios.

3. Use Pythagoras theorem if needed: a² + b² = c²

4. Solve systematically and check units (meters, km).

Exam Tips

• Memorize basic trigonometric ratios and identities.

• Practice heights & distance problems using diagrams.

• Solve previous year NDA, CDS, AFCAT trigonometry questions.

• Focus on speed and accuracy while calculating.