Mathematics is a vital subject that navigation system fall in, hence the key to navigation system's effective, efficient and rapid development is through mathematical progression. The heart of navigation systems solely relies on mathematical application, to calculate the distance, direction and coordinates of any point in earth, without mathematics, calculating coordinates and reaching the exact destination would be highly challenging, hence mathematics, especially in the areas of trigonometry and vectors are essential for all navigation systems known to mankind.
Trigonometry and vectors have major applications in all navigation systems, as they have multiple purposes, from calculating time and distances to determining position using sextants. First of all, these calculations are used to determine the direction a sailor needs to head after taking into consideration the physical factors such as wind and water current. For example, if a sailor needs to sail from Point O to Point A, he must consider the wind speed that affect his sails and the water current that might push him/her to an altered direction. Hence trigonometry could be applied so that the sailor for instance could head 50 degrees west (point B) as a compensation to the current and wind pushing the boat to the east, which would steer to his/her target destination, Point A. Plus, vectors is applied as the sailor could derive that he needs towards head to Point B (50 degrees east of point A) from point O at a certain speed, to reach Point A, which is the resultant vector after being affected by the wind and water current/tide speed. These situations inspired cartographers and navigators build equipment and tools that contribute to navigation, such as the sextant and marine chronometer, which aided humanity significantly in early exploration to various continents, and in globalization and interconnectedness of the whole world. Trigonometry is also applied in a sextant for precisely calculating the angle to steer towards the target destination, while referring to a celestial body (like a star), as a reference point.