Angle Command

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°.

• Vector: Returns the angle between the x‐axis and given vector.

Example: Angle[Vector[(1, 1)]] yields 45°.

• Point: Returns the angle between the x‐axis and the position vector of the given point.

Example: Angle[(1, 1)] yields 45°.

• Number: Converts the number into an angle (result between 0 and 2π).

Example: Angle[20] yields 65.92°.

• Polygon: Creates all angles of a polygon in mathematically positive orientation (i.e., counter clockwise).

Example: Angle[Polygon[(4, 1), (2, 4), (1, 1)] ] yields 56.31°, 52.13° and 71.57°.

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 (between 0° and 360°).

Example:

Angle[Vector[(1, 1)], Vector[(2, 5)]] yields 23.2°.

Angle[ <Line>, <Line> ]

Returns the angle between the direction vectors of two lines (between 0° and 360°).

Example:

Angle[y = x + 2, y = 2x + 3] yields 18.43°.

Angle[ <Point>, <Apex>, <Point> ]

Returns the angle which is defined by the points (between 0° and 360°).

Example:

Angle[(1, 1), (1, 4), (4, 2)] yields 56.31°.

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.

Note: See also Angle and Angle with Given Size tools.