Difference between revisions of "Angle Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} | ||
− | ;Angle | + | ;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''.}} | ||
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− | ;Angle | + | ;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 | + | ;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''.. | ||
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:*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>}} | :*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 | + | ;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''.</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 | + | ;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''.</div>}} | :*<code><nowiki>Angle[2x - y + z = 0, z = 0]</nowiki></code> yields ''114.09°'' or the corresponding value in ''radians''.</div>}} | ||
− | ;Angle | + | ;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>}} | :{{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 | + | ;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 ''30°'' and the point ''(1.9, -1.1)''.</div>}} | :{{example|1=<div>:*<code><nowiki>Angle[(0, 0), (3, 3), 30°]</nowiki></code> yields ''30°'' and the point ''(1.9, -1.1)''.</div>}} | ||
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− | ;Angle | + | ;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.}} |
Revision as of 17:16, 7 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
andg(x) := 2x + 3
then commandAngle[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]
andAngle[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° andAngle[(-1, -1, 0),(0, 0, 0),(1, -1, 0), zAxis]
yields 90° or the corresponding values in radians.
Note: See also Angle and Angle with Given Size tools.