Difference between revisions of "Angle"
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| − | The '''angle''' between two [[line]]s (or line segments) that have a point in common is the amount of rotation that separates the two lines. Note that the lines must have a point in common in order to define an angle between them. | + | The '''angle''' between two [[line]]s (or line segments) that have a point in common is the amount of rotation that separates the two lines from their vertex. Note that the lines must have a point in common in order to define an angle between them. |
Angles were described by [[Euclid]] as "the inclination to one another of two lines which meet each other in the same [[plane]], and do not lie straight with respect to each other" | Angles were described by [[Euclid]] as "the inclination to one another of two lines which meet each other in the same [[plane]], and do not lie straight with respect to each other" | ||
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Degree: Most commonly used in everyday life. It is defined as 1/360 of a full circle, therefore a circle has 360 degrees. | Degree: Most commonly used in everyday life. It is defined as 1/360 of a full circle, therefore a circle has 360 degrees. | ||
| − | Radian: Most commonly used in science and engineering, is the angle subtended by an arc of a circle which have the same length as the circle radius. One full circle is equal to 2 | + | Radian: Most commonly used in science and engineering, is the angle subtended by an arc of a circle which have the same length as the circle radius. One full circle is equal to 2<big><math>\pi</math></big> radians, and one radian is 180/<big><math>\pi</math></big> degrees. |
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| + | Arcminute: Commonly used in [[astronomy]], 1 arcminute is 1/60 of a degree or 1/21600 of a circle. It is useful due to the small angles often encountered. | ||
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| + | Arcsecond: Commonly used in astronomy, 1 arcsecond is 1/60 of an arcminute or 1/1296000 of a circle. | ||
==Classification== | ==Classification== | ||
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* [[Reflex angle|reflex]] (over 180 degrees) | * [[Reflex angle|reflex]] (over 180 degrees) | ||
| + | ==Vectors== | ||
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| + | The angle between two [[vector]]s can be found using the [[dot product]]. | ||
[[Category:Plane Geometry]] | [[Category:Plane Geometry]] | ||
Latest revision as of 12:19, August 25, 2019
The angle between two lines (or line segments) that have a point in common is the amount of rotation that separates the two lines from their vertex. Note that the lines must have a point in common in order to define an angle between them. Angles were described by Euclid as "the inclination to one another of two lines which meet each other in the same plane, and do not lie straight with respect to each other"
Units
There are several units used to measure angles, the most common are:
Degree: Most commonly used in everyday life. It is defined as 1/360 of a full circle, therefore a circle has 360 degrees.
Radian: Most commonly used in science and engineering, is the angle subtended by an arc of a circle which have the same length as the circle radius. One full circle is equal to 2 radians, and one radian is 180/ degrees.
Arcminute: Commonly used in astronomy, 1 arcminute is 1/60 of a degree or 1/21600 of a circle. It is useful due to the small angles often encountered.
Arcsecond: Commonly used in astronomy, 1 arcsecond is 1/60 of an arcminute or 1/1296000 of a circle.
Classification
A simple way to classify angles is the following:
Vectors
The angle between two vectors can be found using the dot product.