Angle Command
From GeoGebra Manual
- 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 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 (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).
- Example:
Angle[(1, 2, 3),(2, 1, 2),(-1, -5, 1), Line[(1, 2, 3),(2, 1, 2)]]
yields 109.91° or the corresponding value in radians.
Note: See also Angle and Angle with Given Size tools.