Editing Angle (section)

===Signed angles <span class="anchor" id="Sign"></span><span class="anchor" id="Positive and negative angles"></span>===
{{main|Angle of rotation}}
{{see also|Sign (mathematics)#Angles|Euclidean space#Angle}}
[[File:Angles on the unit circle.svg|right|thumb|Measuring from the [[x-axis]], angles on the [[unit circle]] count as positive in the [[counterclockwise]] direction, and negative in the [[clockwise]] direction.]]

It is frequently helpful to impose a convention that allows positive and negative angular values to represent [[Orientation (geometry)|orientations]] and/or [[Rotation (mathematics)|rotations]] in opposite directions or "sense" relative to some reference.

In a two-dimensional [[Cartesian coordinate system]], an angle is typically defined by its two sides, with its vertex at the origin. The ''initial side'' is on the positive [[x-axis]], while the other side or ''terminal side'' is defined by the measure from the initial side in radians, degrees, or turns, with ''positive angles'' representing rotations toward the positive [[y-axis]] and ''negative angles'' representing rotations toward the negative ''y''-axis. When Cartesian coordinates are represented by ''standard position'', defined by the ''x''-axis rightward and the ''y''-axis upward, positive rotations are [[anticlockwise]], and negative cycles are [[clockwise]].

In many contexts, an angle of −''θ'' is effectively equivalent to an angle of "one full turn minus ''θ''". For example, an orientation represented as −45° is effectively equal to an orientation defined as 360°&nbsp;−&nbsp;45° or 315°. Although the final position is the same, a physical rotation (movement) of −45° is not the same as a rotation of 315° (for example, the rotation of a person holding a broom resting on a dusty floor would leave visually different traces of swept regions on the floor).

In three-dimensional geometry, "clockwise" and "anticlockwise" have no absolute meaning, so the direction of positive and negative angles must be defined in terms of an [[Orientability|orientation]], which is typically determined by a [[Normal (geometry)|normal vector]] passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie.

In [[navigation]], [[bearing (navigation)|bearings]] or [[azimuth]] are measured relative to north. By convention, viewed from above, bearing angles are positive clockwise, so a bearing of 45° corresponds to a north-east orientation. Negative bearings are not used in navigation, so a north-west orientation corresponds to a bearing of 315°.