Difference between revisions of "Angle Command"

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<noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|geometry}}
 
<noinclude>{{Manual Page|version=4.0}}</noinclude>{{command|geometry}}
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;Angle[ <Object> ]
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*'''Conic:''' Returns the angle of twist of a conic section’s major axis (see command [[Axes Command|Axes]]).
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:{{example|1=<code><nowiki>Angle[x^2 + y^2 = 2]</nowiki></code> yields ''0°''.}}
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*'''Vector:''' Returns the angle between the ''x''‐axis and given vector.
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:{{example|1=<code><nowiki>Angle[Vector[(1, 1)]]</nowiki></code> yields ''45°''.}}
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*'''Point:''' Returns the angle between the ''x''‐axis and the position vector of the given point.
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:{{example|1=<code><nowiki>Angle[(1, 1)]</nowiki></code> yields ''45°''.}}
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*'''Number:''' Converts the number into an angle (result between 0 and 2pi).
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:{{example|1=<code><nowiki>Angle[20]</nowiki></code> yields ''65.92°''.}}
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*'''Polygon:''' Creates all angles of a polygon in mathematically positive orientation (i.e., counter clockwise).
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:{{example|1=<code><nowiki>Angle[Polygon[(4, 1), (2, 4), (1, 1)] ]</nowiki></code> yields ''56.31°'', ''52.13°'' and ''71.57°''.}}
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:{{Note|If the polygon was created in counter clockwise orientation, you get the interior angles. If the polygon was created in clockwise orientation, you get the exterior angles.}}
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;Angle[ <Vector>, <Vector> ]: Returns the angle between two vectors (between 0° and 360°).
 
;Angle[ <Vector>, <Vector> ]: Returns the angle between two vectors (between 0° and 360°).
 
:{{example|1=<div><code><nowiki>Angle[Vector[(1, 1)], Vector[(2, 5)]]</nowiki></code> yields ''23.2°''.</div>}}
 
:{{example|1=<div><code><nowiki>Angle[Vector[(1, 1)], Vector[(2, 5)]]</nowiki></code> yields ''23.2°''.</div>}}
 
;Angle[ <Line>, <Line> ]: Returns the angle between the direction vectors of two lines (between 0° and 360°).
 
;Angle[ <Line>, <Line> ]: Returns the angle between the direction vectors of two lines (between 0° and 360°).
:{{example|1=<div><code><nowiki>Angle[y = x + 2, y = 2x + 3]</nowiki></code> yields ''18.44°''.</div>}}
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:{{example|1=<div><code><nowiki>Angle[y = x + 2, y = 2x + 3]</nowiki></code> yields ''18.43°''.</div>}}
 
;Angle[ <Point>, <Apex>, <Point> ]: Returns the angle which is defined by the points (between 0° and 360°).
 
;Angle[ <Point>, <Apex>, <Point> ]: Returns the angle which is defined by the points (between 0° and 360°).
 
:{{example|1=<div><code><nowiki>Angle[(1, 1), (1, 4), (4, 2)]</nowiki></code> yields ''56.31°''.</div>}}
 
:{{example|1=<div><code><nowiki>Angle[(1, 1), (1, 4), (4, 2)]</nowiki></code> yields ''56.31°''.</div>}}
 
;Angle[ <Point>, <Apex>, <Angle> ]: Returns the angle of size ''α'' drawn from ''point'' with ''apex''.
 
;Angle[ <Point>, <Apex>, <Angle> ]: Returns the angle of size ''α'' drawn from ''point'' with ''apex''.
:{{Note| The point ''Rotate[A, α, B]'' is created as well.}}
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:{{example|1=<div><code><nowiki>Angle[(0, 0), (3, 3), 30°]</nowiki></code> yields ''(1.9, -1.1)''.</div>}}
;Angle[ <Conic> ]: Returns the angle of twist of a conic section’s major axis (see command [[Axes Command|Axes]]) .
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:{{Note| The point ''Rotate[ <Point>, <Angle>, <Apex> ]'' is created as well.}}
;Angle[ <Vector> ]: Returns the angle between the ''x''‐axis and given vector.
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;Angle[ <Point> ]: Returns the angle between the ''x''‐axis and the position vector of the given point.
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{{Note|See also [[File:Tool Angle.gif|16px]] [[Angle Tool|Angle]] and [[File:Tool Angle Fixed.gif|16px]] [[Angle with Given Size Tool|Angle with Given Size]] tools.}}
;Angle[ <Number> ]: Converts the number into an angle (result between 0 and 2pi).
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;Angle[ <Polygon> ]: Creates all angles of a polygon in mathematically positive orientation (i.e., counter clockwise).
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:{{Note|If the polygon was created in counter clockwise orientation, you get the interior angles. If the polygon was created in clockwise orientation, you get the exterior angles.}}
 
:{{Note|See also [[File:Tool Angle.gif|16px]] [[Angle Tool|Angle]] and [[File:Tool Angle Fixed.gif|16px]] [[Angle with Given Size Tool|Angle with Given Size]] tools .}}
 
 
{{betamanual|version=5.0|{{Note|1=From GeoGebra 5, this command will work in 3D as well}}
 
{{betamanual|version=5.0|{{Note|1=From GeoGebra 5, this command will work in 3D as well}}
 
}}
 
}}

Revision as of 09:27, 18 July 2013


Angle[ <Object> ]
  • Conic: Returns the angle of twist of a conic section’s major axis (see command Axes).
Example: Angle[x^2 + y^2 = 2] yields .
  • Vector: Returns the angle between the x‐axis and given vector.
Example: Angle[Vector[(1, 1)]] yields 45°.
  • Point: Returns the angle between the x‐axis and the position vector of the given point.
Example: Angle[(1, 1)] yields 45°.
  • Number: Converts the number into an angle (result between 0 and 2pi).
Example: Angle[20] yields 65.92°.
  • Polygon: Creates all angles of a polygon in mathematically positive orientation (i.e., counter clockwise).
Example: Angle[Polygon[(4, 1), (2, 4), (1, 1)] ] yields 56.31°, 52.13° and 71.57°.
Note: If the polygon was created in counter clockwise orientation, you get the interior angles. If the polygon was created in clockwise orientation, you get the exterior angles.


Angle[ <Vector>, <Vector> ]
Returns the angle between two vectors (between 0° and 360°).
Example:
Angle[Vector[(1, 1)], Vector[(2, 5)]] yields 23.2°.
Angle[ <Line>, <Line> ]
Returns the angle between the direction vectors of two lines (between 0° and 360°).
Example:
Angle[y = x + 2, y = 2x + 3] yields 18.43°.
Angle[ <Point>, <Apex>, <Point> ]
Returns the angle which is defined by the points (between 0° and 360°).
Example:
Angle[(1, 1), (1, 4), (4, 2)] yields 56.31°.
Angle[ <Point>, <Apex>, <Angle> ]
Returns the angle of size α drawn from point with apex.
Example:
Angle[(0, 0), (3, 3), 30°] yields (1.9, -1.1).
Note: The point Rotate[ <Point>, <Angle>, <Apex> ] is created as well.
Note: See also Tool Angle.gif Angle and Tool Angle Fixed.gif Angle with Given Size tools.


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