# Direction angle

Definition of the direction angle

Direction angle (usually denoted by) is a term used in mathematics and geodesy for the angle between the north direction ( grid north ) and a straight line or line . The directional angle of a line from point to point is given from the parallel to the north-facing x-axis through the point to the right, i.e. clockwise. ${\ displaystyle t}$${\ displaystyle A}$${\ displaystyle E}$${\ displaystyle A}$

In navigation , the direction angle is referred to as the course angle , compass angle or march number. It means the same size.

## calculation

Common spellings for the direction angle are or . The index denotes the starting point or position and the second index the end or destination point. ${\ displaystyle t_ {A} ^ {E}}$${\ displaystyle t_ {A, E}}$${\ displaystyle A}$${\ displaystyle E}$

For the direction angle in a geodetic coordinate system , i.e. H. with geodetically positive or mathematically negative direction of rotation , the following relationship applies:

${\ displaystyle \ tan t_ {A} ^ {E} = {\ frac {y_ {E} -y_ {A}} {x_ {E} -x_ {A}}} = {\ frac {\ Delta y} { \ Delta x}}.}$

When calculating polar coordinates from Cartesian coordinates, the quadrant in which the direction angle lies must be taken into account. The function is suitable for this : ${\ displaystyle \ operatorname {arctan}}$

${\ displaystyle t_ {A} ^ {E} = \ operatorname {arctan} {y_ {E} -y_ {A} \ over x_ {E} -x_ {A}} = \ operatorname {arctan} {\ Delta y \ over \ Delta x}}$