# Direction

- Author:
- Lukas Kurt Schenk

If we have a vector finding the magnitude is easy.
The formular we need is tan( )= .
We can rewrite this formular so we get the angle: =arctan( ).
You may find the arc tangent on your calcuator as tan .
If the vector is parallel to one axis, we can determine the angle by looking at the parallel axis and the direction it is pointing:
Parallel to x-axis:
Points to the right -> 0°
Points to the left -> 180°
Parallel to the y-axis:
Points upwards -> 90°
Points downwards -> 270°
In the other cases we need to calculate the angle and take a look in which direction the vector points.
Upper right: we can take the angle as we got it from our formular
Down right: we need to add +360° to our angle.
left: we need to add +180° to our angle.
For Example: we get -54 degrees for our angle and it points to the left we calculate: -54°+180°= 126°
Exercise: Move the slider and watch how the angle is calculated. If you know the solution, you can check it everytime.