Difference between revisions of "Angle Command"
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;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[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''. | ||
::and in '''CAS View''' : | ::and in '''CAS View''' : | ||
− | :::*<code><nowiki>Angle[x + 2, 2x + 3]</nowiki></code> yields | + | :::*<code><nowiki>Angle[x + 2, 2x + 3]</nowiki></code> yields <math>acos(3 \cdot \frac{\sqrt{10}}{10})</math>.<br/> or |
− | :::*<code><nowiki>f(x) := x + 2</nowiki></code> <br/> <code><nowiki>g(x) := 2x + 3</nowiki></code> <br/> <code><nowiki>Angle[f(x) , g(x)]</nowiki></code> yields | + | :::*<code><nowiki>f(x) := x + 2</nowiki></code> <br/> <code><nowiki>g(x) := 2x + 3</nowiki></code> <br/> <code><nowiki>Angle[f(x) , g(x)]</nowiki></code> yields <math>acos(3 \cdot \frac{\sqrt{10}}{10})</math>. |
</div>}} | </div>}} | ||
Revision as of 22:47, 12 December 2015
- 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(3 \cdot \frac{\sqrt{10}}{10}).
orf(x) := x + 2
g(x) := 2x + 3
Angle[f(x) , g(x)]
yields acos(3 \cdot \frac{\sqrt{10}}{10}).
- 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[Line[(1, 2, 3),(-2, -2, 0)], Plane[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[Plane[2x - y + z = 0], Plane[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).Angle[Point[{0, 0}], Point[{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.