🧭 Direction Sense - Formula Sheet

🎯 Basic Directions

Main Directions

N (North)     ↑
E (East)      →
S (South)     ↓
W (West)      ←

Sub-directions

NE (North-East)   ↗
NW (North-West)   ↖
SE (South-East)   ↘
SW (South-West)   ↙

Angle Relationships

Each main direction = 90° apart
Each sub-direction = 45° from main directions

📊 Rotation Rules

Right Turn (90° clockwise)

North → East → South → West → North

Left Turn (90° anticlockwise)

North → West → South → East → North

Multiple Rotations

Right × 2 = 180° turn (opposite direction)
Right × 3 = 270° turn = Left × 1
Right × 4 = 360° turn = original direction

🔢 Distance Calculations

Pythagoras Theorem

Distance² = (North-South distance)² + (East-West distance)²
Distance = √[(NS)² + (EW)²]

Shadow Problems

Morning: Sun in East → Shadow to West
Evening: Sun in West → Shadow to East
Noon: Sun overhead → No shadow

⚡ Solving Approach

Step-by-Step Method

1. Draw starting point
2. Mark each movement with direction and distance
3. Track final position
4. Calculate required distance/direction

Coordinate Method

Let starting point = (0,0)
North: +y, South: -y
East: +x, West: -x
Final position = (x₁ + x₂ + ..., y₁ + y₂ + ...)

📝 Quick Tips

1. Always draw a diagram
2. Use coordinate system for accuracy
3. Remember: Right = clockwise, Left = anticlockwise
4. Final position = Sum of all movements
5. Use Pythagoras for straight-line distance

Master Direction Sense - Draw diagrams, use Pythagoras! 🧭