Angle Command

Angle( <Object> )

Conic: Returns the angle of twist of a conic section’s major axis (see command Axes).

Angle(x²/4+y²/9=1) yields 90° or 1.57 if the default angle unit is radians.

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.

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.

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).

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).

Angle(Polygon((4, 1), (2, 4), (1, 1))) yields 56.31°, 52.13° and 71.57° or the corresponding values in radians.

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((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).

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.

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.

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).

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.

Angle((0, 0), (3, 3), 30°) yields 30° and the point (1.9, -1.1).

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((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.

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.

See also Angle and Angle with Given Size tools.