Difference between revisions of "Angle Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
;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]]).
:{{example|1=<code><nowiki>Angle[x²/4+y²/9=1]</nowiki></code> yields ''90°'' or ''1.57'' if the default angle unit is ''radians''.}}
+
:{{example|1=<code><nowiki>Angle(x²/4+y²/9=1)</nowiki></code> yields ''90°'' or ''1.57'' if the default angle unit is ''radians''.}}
 
{{Note|It is not possible to change the Angle Unit to Radian in GeoGebra 5.0 Web and Tablet App Version.}}
 
{{Note|It is not possible to change the Angle Unit to Radian in GeoGebra 5.0 Web and Tablet App Version.}}
 
*'''Vector:''' Returns the angle between the ''x''‐axis and given vector.
 
*'''Vector:''' Returns the angle between the ''x''‐axis and given vector.
:{{example|1=<code><nowiki>Angle[Vector[(1, 1)]]</nowiki></code> yields ''45°'' or the corresponding value in ''radians''.}}
+
:{{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.
:{{example|1=<code><nowiki>Angle[(1, 1)]</nowiki></code> yields ''45°'' or the corresponding value in ''radians''.}}
+
:{{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 in [0,360°] or [0,2π] depending on the default angle unit).
 
*'''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°'' when the default unit for angles is ''degrees''.}}
+
:{{example|1=<code><nowiki>Angle(20)</nowiki></code> yields ''65.92°'' when the default unit for angles is ''degrees''.}}
 
*'''Polygon:''' Creates all angles of a polygon in mathematically positive orientation (counter clockwise).
 
*'''Polygon:''' Creates all angles of a polygon in mathematically positive orientation (counter clockwise).
:{{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''.}}
+
:{{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.}}
  
  
;Angle[ <Vector>, <Vector> ]: Returns the angle between two vectors (result in [0,360°] or [0,2π] depending on the default angle unit).
+
;Angle( <Vector>, <Vector> ): Returns the angle between two vectors (result in [0,360°] or [0,2π] depending on the default angle unit).
:{{example|1=<div><code><nowiki>Angle[Vector[(1, 1)], Vector[(2, 5)]]</nowiki></code> yields ''23.2°'' or the corresponding value in ''radians''.</div>}}
+
:{{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 (result in [0,360°] or [0,2π] depending on the default angle unit).
+
;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|1=<div>
 
:{{example|1=<div>
:*<code><nowiki>Angle[y = x + 2, y = 2x + 3]</nowiki></code> yields ''18.43°'' or the corresponding value in ''radians''.
+
:*<code><nowiki>Angle(y = x + 2, y = 2x + 3)</nowiki></code> yields ''18.43°'' or the corresponding value in ''radians''..
:*<code><nowiki>Angle[f(x) = x + 2, g(x) = 2x + 3]</nowiki></code> yields ''18.43°'' or the corresponding value in ''radians''.
+
:*<code><nowiki>Angle(Line((-2, 0, 0), (0, 0, 2)), Line((2, 0, 0), (0, 0, 2)))</nowiki></code> yields ''90°'' or the corresponding value in ''radians''.
:*<code><nowiki>Angle[Line[(-2, 0, 0), (0, 0, 2)], Line[(2, 0, 0), (0, 0, 2)]]</nowiki></code> yields ''90°'' or the corresponding value in ''radians''.</div>}}
+
::and in ''CAS View'' :
 +
:*<code><nowiki>Angle(x + 2, 2x + 3)</nowiki></code> yields <math>acos \left( 3 \cdot \frac{\sqrt{10}}{10} \right)</math>.
 +
:*Define <code><nowiki>f(x) := x + 2</nowiki></code>  and <code><nowiki>g(x) := 2x + 3</nowiki></code> then command <code><nowiki>Angle(f(x), g(x))</nowiki></code> yields <math>acos \left(3 \cdot \frac{\sqrt{10}}{10} \right)</math>.</div>}}
  
;Angle[ <Line>, <Plane> ]: Returns the angle between the line and the plane.
+
;Angle( <Line>, <Plane> ): Returns the angle between the line and the plane.
 
:{{example|1=<div>
 
:{{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''.
+
:*<code><nowiki>Angle(Line((1, 2, 3),(-2, -2, 0)), z = 0)</nowiki></code> yields ''30.96°'' or the corresponding value in ''radians''.</div>}}
:*<code><nowiki>Angle[Line[(1, 2, 3),(-2, -2, 0)], Plane[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.
 
 
;Angle[ <Plane>, <Plane> ]: Returns the angle between the two given planes.
 
 
:{{example|1=<div>
 
:{{example|1=<div>
:*<code><nowiki>Angle[2x - y + z = 0, z = 0]</nowiki></code> yields ''114.09°'' or the corresponding value in ''radians''.
+
:*<code><nowiki>Angle(2x - y + z = 0, z = 0)</nowiki></code> yields ''114.09°'' or the corresponding value in ''radians''.</div>}}
:*<code><nowiki>Angle[Plane[2x - y + z = 0], Plane[z = 0]]</nowiki></code> yields ''114.09°'' or the corresponding value in ''radians''.</div>}}
+
;Angle( <Point>, <Apex>, <Point> ): Returns the angle defined by the given 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>, <Point> ]: Returns the angle defined by the given points (result in [0,360°] or [0,2π] depending on the default angle unit).
+
;Angle( <Point>, <Apex>, <Angle> ): Returns the angle of size ''α'' drawn from ''point'' with ''apex''.
:{{example|1=<div><code><nowiki>Angle[(1, 1), (1, 4), (4, 2)]</nowiki></code> yields ''56.31°'' or the corresponding value in ''radians''.</div>}}
+
:{{example|1=<div>:*<code><nowiki>Angle((0, 0), (3, 3), 30°)</nowiki></code> yields ''30°'' and the point ''(1.9, -1.1)''.</div>}}
  
;Angle[ <Point>, <Apex>, <Angle> ]: Returns the angle of size ''α'' drawn from ''point'' with ''apex''.
+
:{{Note| The point ''Rotate( <Point>, <Angle>, <Apex> )'' is created as well.}}
:{{example|1=<div>
 
:*<code><nowiki>Angle[(0, 0), (3, 3), 30°]</nowiki></code> yields ''30°'' and the point ''(1.9, -1.1)''.
 
:*<code><nowiki>Angle[Point[{0, 0}], Point[{3, 3}], 30°]</nowiki></code> yields ''30°'' and the point ''(1.9, -1.1)''.</div>}}
 
:{{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 may be a line or a plane (result in [0,360°] or [0,2π] depending on the default angle unit).
+
;Angle( <Point>, <Point>, <Point>, <Direction> ): Returns the angle defined by the points and the given ''Direction'', that may be a line or a plane (result in [0,360°] or [0,2π] depending on the default angle unit).
:{{note|1=Using a ''Direction'' allows to bypass the standard display of angles in 3''D'' which can be set as just [0,180°] or [180°,360°], so that given three points ''A'', ''B'', ''C'' in 3''D'' the commands <code><nowiki>Angle[A, B, C]</nowiki></code> and <code><nowiki>Angle[C, B, A]</nowiki></code> return their real measure instead of the one restricted to the set intervals.}}
+
:{{note|1=Using a ''Direction'' allows to bypass the standard display of angles in 3''D'' which can be set as just [0,180°] or [180°,360°], so that given three points ''A'', ''B'', ''C'' in 3''D'' the commands <code><nowiki>Angle(A, B, C)</nowiki></code> and <code><nowiki>Angle(C, B, A)</nowiki></code> return their real measure instead of the one restricted to the set intervals.}}
:{{example|1=<div><code><nowiki>Angle[(1, -1, 0),(0, 0, 0),(-1, -1, 0), zAxis]</nowiki></code> yields ''270°'' and <code><nowiki>Angle[(-1, -1, 0),(0, 0, 0),(1, -1, 0), zAxis]</nowiki></code> yields ''90°''  or the corresponding values in ''radians''.</div>}}
+
:{{example|1=<div><code><nowiki>Angle((1, -1, 0),(0, 0, 0),(-1, -1, 0), zAxis)</nowiki></code> yields ''270°'' and <code><nowiki>Angle((-1, -1, 0),(0, 0, 0),(1, -1, 0), zAxis)</nowiki></code> yields ''90°''  or the corresponding values in ''radians''.</div>}}
  
 
{{Note|See also [[File:Mode angle.svg|link=|20px]] [[Angle Tool|Angle]] and [[File:Mode anglefixed.svg|link=|20px]] [[Angle with Given Size Tool|Angle with Given Size]] tools.}}
 
{{Note|See also [[File:Mode angle.svg|link=|20px]] [[Angle Tool|Angle]] and [[File:Mode anglefixed.svg|link=|20px]] [[Angle with Given Size Tool|Angle with Given Size]] tools.}}

Latest revision as of 08:51, 11 October 2017


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.
Note: It is not possible to change the Angle Unit to Radian in GeoGebra 5.0 Web and Tablet App Version.
  • 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° when the default unit for angles is degrees.
  • 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((-2, 0, 0), (0, 0, 2)), Line((2, 0, 0), (0, 0, 2))) yields 90° or the corresponding value in radians.
and in CAS View :
  • Angle(x + 2, 2x + 3) yields acos \left( 3 \cdot \frac{\sqrt{10}}{10} \right).
  • Define f(x) := x + 2 and g(x) := 2x + 3 then command Angle(f(x), g(x)) yields acos \left(3 \cdot \frac{\sqrt{10}}{10} \right).


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 defined by the given 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 30° and the point (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 may be a line or a plane (result in [0,360°] or [0,2π] depending on the default angle unit).
Note: Using a Direction allows to bypass the standard display of angles in 3D which can be set as just [0,180°] or [180°,360°], so that given three points A, B, C in 3D the commands Angle(A, B, C) and Angle(C, B, A) return their real measure instead of the one restricted to the set intervals.
Example:
Angle((1, -1, 0),(0, 0, 0),(-1, -1, 0), zAxis) yields 270° and Angle((-1, -1, 0),(0, 0, 0),(1, -1, 0), zAxis) yields 90° or the corresponding values in radians.


Note: See also Mode angle.svg Angle and Mode anglefixed.svg Angle with Given Size tools.
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