D. Latitudes and Departures
1. Definition; Equations
Latitude is the northsouth component of a line; departure the eastwest. North latitudes are positive, South are negative; similarly East departures are positive, West are negative.
(a) 
(b) 
Figure D1 Latitudes and Departures 
Latitude (Lat) and Departure (Dep) are computed from:
Equations D1 and D2 
Dir can be either a bearing angle, Figure D2(a), or azimuth angle, Figure D2(b).
(a) 
(b) 
Figure D2 Bearings or Azimuths 
Because a bearing angle never exceeds 90°, the Lat and Dep equations will always return positive values.
Sin(0°) to Sin(90°) ranges from 0 to +1.0 Cos(0°) to Cos(90°) ranges from +1.0 to 0 The correct mathematical sign for the Lat and Dep come from the bearing quadrant. A bearing of S 47°35' E has a negative Lat (South) and a positive Dep (East). 

Figure D3 Quadrants 
An azimuth angle ranges from 0° to 360°, so the sine and cosine return the correct signs on the Lat and Dep.
Examples
Figure D4 NE Azimuth 

Figure D5 SW Azimuth 
Reversing a line direction results in the same magnitude Lat and Dep but reversed signs:
Line A to B  Line B to A 
(a)  (b) 
Figure D6 Reverse Latitude and Departure 