Final answer:
To convert compass directions to standard angles measured from the positive x-axis, we rotate the angles accordingly. Examples provided are N36.2°E to 53.8°, 21.7° S of W to 201.7°, and a compass bearing of 274° to 86°. The negative angle −18° converts to 342°.
Step-by-step explanation:
To convert vector directions into standard mathematical angles, which are measured counterclockwise from the positive x-axis, we need to consider the compass directions as starting points and integrate the given angles. Here are the conversions for the directions you provided:
- N36.2°E - Start from the north (90° from the positive x-axis) and rotate 36.2° towards the east. The standard angle is 90° - 36.2° = 53.8°.
- 21.7° S of W - Start from the west (180° from the positive x-axis) and rotate 21.7° towards the south. The standard angle is 180° + 21.7° = 201.7°.
- 274° compass - Compass bearings are measured clockwise from the north. Therefore, the standard mathematical angle is 360° - 274° = 86°.
- −18° - A negative angle suggests a clockwise rotation from the positive x-axis. To convert this to the standard angle, add 360° to the negative angle: 360° - 18° = 342°.
Now, to express 44.7° in different directional terms, we might say:
- N44.7°E - North 44.7° East
- E45.3°N - East 45.3° North (since 90° - 44.7° = 45.3°)
- Compass bearing of 44.7° (since it is already less than 90°, it represents the angle clockwise from north)