🔍 Key Concepts

• Great circle sailing formulas relating distance, latitude, and difference of longitude • Converting west and east longitudes to a correct difference of longitude, especially when they are on opposite sides of the 180° meridian • Using the spherical law of cosines to find great circle distance and then the initial course

💭 Think About

• First, convert both positions so you clearly see which hemisphere each is in and carefully determine the correct difference of longitude—does it cross 180° or not? • After finding the central angle between the two positions using the appropriate formula, how do you turn that angle into distance in nautical miles? • Once you have the great circle distance, use the correct trig relationship to find the initial course at the departure latitude—what must you do with signs for N/S latitudes and E/W longitudes?

✅ Before You Answer

• Be sure your difference of longitude (DLo) is less than or equal to 180° by choosing the smaller arc between longitudes • Confirm that all angles are converted to radians or kept in degrees consistently in your calculator work • After calculating, check that your initial course makes sense: from 08°53.0'N, 79°31.0'W to 33°51.5'S, 151°13.0'E, should the initial true course be generally northwest, southwest, northeast, or southeast?