A significant problem of routing protocols in the Flying Ad Hoc Networks (FANET) is a significant overhead cost due to the high mobility of networking nodes. The problem is caused by a need to send information messages about locations of unmanned aerial vehicles (UAVs). In order to reduce the amount of service information, the following trajectory approximation algorithms have been investigated: an algorithm for conjugating courses and an algorithm based on continuous piecewise-linear functions (CPLF). Four modifications of the CPLF-based algorithm are considered, which differ in the type of piecewise linear function used: basic CPLF, generalized CPLF, generalized CPLF with a compact notation form, and adaptive CPLF. The disadvantages of each algorithm are analyzed. The CPLF approximation of a fragment of an aircraft trajectory consisting of two straight sections and a curved section with variable steepness between them is performed. It is established that adaptive CPLF with variable step reduces the error of trajectory approximation due to the location of most points on the curved sections of the aircraft maneuvering. The modified version of ADV routing protocol has shown a lower overhead value (the gain for small pause time values reaches 23 %). Thus, the effectiveness of the proposed approximation-based routing in FANET is shown.