Direction Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard

A ship sails

N30°E

(30° east of north). Express this direction as a unit vector in the standard

(x, y)

coordinate system where x is east and y is north.

Solution

1
Step 1: $N30°E$ means 30° from north towards east. The angle from the positive y-axis (north) is 30° clockwise.
2
Step 2: Convert to standard angle from positive x-axis: $\theta = 90° - 30° = 60°$ .
3
Step 3: Unit vector: $(\cos 60°, \sin 60°) = (0.5,\ \sqrt{3}/2) \approx (0.5,\ 0.866)$ .

Answer

(0.5,\ \sqrt{3}/2) \approx (0.5,\ 0.866)

Compass bearings are measured clockwise from north, while standard math angles are measured counterclockwise from the positive x-axis. Converting between them: standard angle