Difference between revisions of "Angle Command"

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(if we want to give an example, it is more intelligent if it is serious)
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;Angle[ <Object> ]
 
;Angle[ <Object> ]
 
*'''Conic:''' Returns the angle of twist of a conic section’s major axis (see command [[Axes Command|Axes]]).
 
*'''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[x²/4+y²/9=1]</nowiki></code> yields ''90°''.}}
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:{{example|1=<code><nowiki>Angle[x²/4+y²/9=1]</nowiki></code> yields ''90°'' or 1.57 if the default angle unit is ''radians''.}}
 
*'''Vector:''' Returns the angle between the ''x''‐axis and given vector.
 
*'''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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:{{example|1=<code><nowiki>Angle[Vector[(1, 1)]]</nowiki></code> yields ''45°'' or the corresponding value in ''radians''.}}
 
*'''Point:''' Returns the angle between the ''x''‐axis and the position vector of the given point.
 
*'''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°''.}}
+
:{{example|1=<code><nowiki>Angle[(1, 1)]</nowiki></code> yields ''45°'' or the corresponding value in ''radians''.}}
−
*'''Number:''' Converts the number into an angle (result between 0 and 2π).
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*'''Number:''' Converts the number into an angle (result in [0,360°] or [0,2π] depending on the default angle unit).
−
:{{example|1=<code><nowiki>Angle[20]</nowiki></code> yields ''65.92°''.}}
+
:{{example|1=<code><nowiki>Angle[20]</nowiki></code> yields ''65.92°'' or the corresponding value in ''radians''.}}
−
*'''Polygon:''' Creates all angles of a polygon in mathematically positive orientation (i.e., counter clockwise).
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*'''Polygon:''' Creates all angles of a polygon in mathematically positive orientation (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°''.}}
+
:{{example|1=<code><nowiki>Angle[Polygon[(4, 1), (2, 4), (1, 1)] ]</nowiki></code> yields ''56.31°'', ''52.13°'' and ''71.57°'' or the corresponding values in ''radians''.}}
 
:{{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|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°).
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;Angle[ <Vector>, <Vector> ]: Returns the angle between two vectors (result in [0,360°] or [0,2π] depending on the default angle unit).
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:{{example|1=<div><code><nowiki>Angle[Vector[(1, 1)], Vector[(2, 5)]]</nowiki></code> yields ''23.2°''.</div>}}
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:{{example|1=<div><code><nowiki>Angle[Vector[(1, 1)], Vector[(2, 5)]]</nowiki></code> yields ''23.2°'' or the corresponding value in ''radians''.</div>}}
−
;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 ''18.43°''.</div>}}
+
;Angle[ <Line>, <Line> ]: Returns the angle between the direction vectors of two lines (result in [0,360°] or [0,2π] depending on the default angle unit).
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;Angle[ <Point>, <Apex>, <Point> ]: Returns the angle which is defined by the points (between 0° and 360°).
+
:{{example|1=<div><code><nowiki>Angle[y = x + 2, y = 2x + 3]</nowiki></code> yields ''18.43°'' or the corresponding value in ''radians''.</div>}}
−
:{{example|1=<div><code><nowiki>Angle[(1, 1), (1, 4), (4, 2)]</nowiki></code> yields ''56.31°''.</div>}}
+
 
 +
;Angle[ <Line>, <Plane> ]: Returns the angle between the line and the plane.
 +
:{{example|1=<div><code><nowiki>Angle[Line[(1, 2, 3),(-2, -2, 0)], z = 0]</nowiki></code> yields ''30.96°'' or the corresponding value in ''radians''.</div>}}
 +
 
 +
;Angle[ <Plane>, <Plane> ]: Returns the angle between the two given planes.
 +
:{{example|1=<div><code><nowiki>Angle[2x - y + z = 0, z = 0]</nowiki></code> yields ''114.09°'' or the corresponding value in ''radians''.</div>}}
 +
 
 +
;Angle[ <Point>, <Apex>, <Point> ]: Returns the angle which is defined by the points (result in [0,360°] or [0,2π] depending on the default angle unit).
 +
:{{example|1=<div><code><nowiki>Angle[(1, 1), (1, 4), (4, 2)]</nowiki></code> yields ''56.31°'' or the corresponding value in ''radians''.</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''.
 
:{{example|1=<div><code><nowiki>Angle[(0, 0), (3, 3), 30°]</nowiki></code> yields ''(1.9, -1.1)''.</div>}}
 
:{{example|1=<div><code><nowiki>Angle[(0, 0), (3, 3), 30°]</nowiki></code> yields ''(1.9, -1.1)''.</div>}}
 
:{{Note| The point ''Rotate[ <Point>, <Angle>, <Apex> ]'' is created as well.}}
 
:{{Note| The point ''Rotate[ <Point>, <Angle>, <Apex> ]'' is created as well.}}
 +
 +
;Angle[ <Point>, <Point>, <Point>, <Direction> ]: Returns the angle defined by the points and the given Direction, that can be a line or a plane (result in [0,360°] or [0,2π] depending on the default angle unit).
 +
:{{example|1=<div><code><nowiki>Angle[(1, 1), (1, 4), (4, 2)]</nowiki></code> yields ''56.31°'' or the corresponding value in ''radians''.</div>}}
  
 
{{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.}}
 
{{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.}}
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−
 
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{{betamanual|version=5.0|{{Note|1=From GeoGebra 5, this command will work in 3D as well}}
 
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}}
 

Revision as of 11:42, 23 March 2015

Angle

This article is about GeoGebra command.

Command Categories (All commands)


Angle[ <Object> ]
  • Conic: Returns the angle of twist of a conic section’s major axis (see command Axes).
Example: Angle[x²/4+y²/9=1] yields 90° or 1.57 if the default angle unit is radians.
  • Vector: Returns the angle between the x‐axis and given vector.
Example: Angle[Vector[(1, 1)]] yields 45° or the corresponding value in radians.
  • Point: Returns the angle between the x‐axis and the position vector of the given point.
Example: Angle[(1, 1)] yields 45° or the corresponding value in radians.
  • Number: Converts the number into an angle (result in [0,360°] or [0,2π] depending on the default angle unit).
Example: Angle[20] yields 65.92° or the corresponding value in radians.
  • Polygon: Creates all angles of a polygon in mathematically positive orientation (counter clockwise).
Example: Angle[Polygon[(4, 1), (2, 4), (1, 1)] ] yields 56.31°, 52.13° and 71.57° or the corresponding values in radians.
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 (result in [0,360°] or [0,2π] depending on the default angle unit).
Example:
Angle[Vector[(1, 1)], Vector[(2, 5)]] yields 23.2° or the corresponding value in radians.


Angle[ <Line>, <Line> ]
Returns the angle between the direction vectors of two lines (result in [0,360°] or [0,2π] depending on the default angle unit).
Example:
Angle[y = x + 2, y = 2x + 3] yields 18.43° or the corresponding value in radians.


Angle[ <Line>, <Plane> ]
Returns the angle between the line and the plane.
Example:
Angle[Line[(1, 2, 3),(-2, -2, 0)], z = 0] yields 30.96° or the corresponding value in radians.


Angle[ <Plane>, <Plane> ]
Returns the angle between the two given planes.
Example:
Angle[2x - y + z = 0, z = 0] yields 114.09° or the corresponding value in radians.


Angle[ <Point>, <Apex>, <Point> ]
Returns the angle which is defined by the points (result in [0,360°] or [0,2π] depending on the default angle unit).
Example:
Angle[(1, 1), (1, 4), (4, 2)] yields 56.31° or the corresponding value in radians.


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.
Angle[ <Point>, <Point>, <Point>, <Direction> ]
Returns the angle defined by the points and the given Direction, that can be a line or a plane (result in [0,360°] or [0,2π] depending on the default angle unit).
Example:
Angle[(1, 1), (1, 4), (4, 2)] yields 56.31° or the corresponding value in radians.


Note: See also Tool Angle.gif Angle and Tool Angle Fixed.gif Angle with Given Size tools.
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