- Draw angles in standard position.
- Convert between degrees and radians.
- Convert angles between decimal form and degree, minutes, and seconds form
- Find coterminal angles.
- Find complementary and supplementary angles
Angles are measured differently in navigation. While mathematicians measure angles counterclockwise from the positive x-axis (east), navigators measure angles clockwise from north. Understanding how to convert between these two systems is essential for pilots, sailors, surveyors, and anyone working with maps and GPS systems. In this page, you’ll learn to work with both systems and convert between them.
In mathematics, angles in standard position have:
- Vertex at the origin
- Initial side along the positive x-axis (pointing east)
- Positive angles measured counterclockwise
- Angles measured from 0° to 360°
Aircraft Navigation and Heading
Pilots use heading to describe the direction an aircraft is pointed, measured as an angle in standard position from north (0°). A heading of 90° means the aircraft points due east, 180° means due south, and 270° means due west.
bearing from North
A navigation angle measured clockwise from north, ranging from 0° to 360°, where 0° is north, 90° is east, 180° is south, and 270° is west.
How To: Drawing Angles for Navigation Heading
- Determine which quadrant the angle belongs in (Quadrant I: 0°-90°, Quadrant II: 90°-180°, Quadrant III: 180°-270°, Quadrant IV: 270°-360°)
- Place the vertex at the origin with the initial side along the positive x-axis (pointing east)
- Rotate counterclockwise the appropriate amount
- Draw the terminal side proportionately within the correct quadrant
- An aircraft’s heading is 30° in mathematical standard position. Find the bearing from north.
- A ship travels on a bearing of 120° from north. What is this angle in mathematical standard position?
The direction an aircraft is pointed, expressed as an angle measured clockwise from north in standard position.