🔍 Key Concepts

• Great-circle sailing formulas using latitudes and the difference of longitude • Converting degrees and minutes to decimal degrees before using trigonometric functions • Interpreting the signs of latitude and longitude (N/S, E/W) to get the correct initial course quadrant

💭 Think About

• How does changing from Northern to Southern Hemisphere affect the great-circle track and the approximate direction (NW, SW, etc.) from the starting point? • Before doing any detailed math, if you sketch the two positions on a world map, in which general direction from San Francisco (near 37° N, 122° W) is Sydney (near 34° S, 151° E)? • Once you compute the central angle between the two points (in degrees of arc), how do you convert that angle into nautical miles of great-circle distance?

✅ Before You Answer

• Verify both positions are correctly converted to decimal degrees and that West longitudes are treated as negative and East as positive (or vice versa consistently). • Check that the difference of longitude (Δλ) is measured the shorter way around the globe (use 360° − Δλ if needed). • After you find the initial great-circle course angle, confirm whether its quadrant (e.g., southwest, northwest) matches the rough sketch between the two locations.