Definition:Angle/Directed versus Undirected
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Definition
The most basic definition of angle is an undirected angle on the interval $\closedint {0 \degrees} {180 \degrees}$ or $\closedint 0 \pi$.
This definition is often insufficient, in cases such as the external angles of a polygon.
Therefore, angles are most commonly defined in one of two ways:
- $(1): \quad$ Undirected angles on the interval $\closedint {0 \degrees} {360 \degrees}$ or $\closedint 0 {2 \pi}$.
- $(2): \quad$ Directed angles, with the positive direction being anticlockwise from a given line (or, if no line is specified, from the $x$-axis).
- This definition is more commonly found in applied mathematics, such as in surveying, navigation, or, more colloquially, in a $720 \degrees$ degree spin in skateboarding, skiing, etc.
Sources
- 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $1$. Functions: $1.5$ Trigonometric or Circular Functions: $1.5.1$ Unit Circle