angle - Maple Help

Units of Angle

Description

 • An angle symbolically has dimension $1$. For consistency in the Units package, angles have the dimension length/length(radius). The SI derived unit of angle is the radian, which is defined as the angle for which the radius equals the arclength.
 • Maple knows the units of angle listed in the following table.

 Name Symbols Context Alternate Spellings Prefixes radian rad SI * radians SI degree deg, arcdeg @ angle * degrees minute min, arcmin @ angle degrees second s, arcsec @ angle degrees revolution rev angle * revolutions gon angle * gons grade angle * grades, grad, grads mil angle mils mil military mils circle angle circles semicircle angle semicircles quadrant angle quadrants sign angle signs point angle points hour angle hours

 An asterisk ( * ) indicates the default context, an at sign (@) indicates an abbreviation, and under the prefixes column, SI indicates that the unit takes all SI prefixes, IEC indicates that the unit takes IEC prefixes, and SI+ and SI- indicate that the unit takes only positive and negative SI prefixes, respectively.  Refer to a unit in the Units package by indexing the name or symbol with the context, for example, radian[SI] or rev[angle]; or, if the context is indicated as the default, by using only the unit name or symbol, for example, radian or rev.
 The units of angle are defined as follows.
 A degree is defined as $\frac{\mathrm{\pi }}{180}$ radian.
 A minute is defined as $\frac{1}{60}$ degree.
 A second is defined as $\frac{1}{60}$ minute.
 A revolution is defined as $2\mathrm{Pi}$ radians.
 A gon, grade, or grad is defined by the relationship: $100$ grades equals $\frac{\mathrm{\pi }}{2}$ radians.
 An angular mil is defined as $\frac{1}{1000}$ radian.
 A military mil is defined as $\frac{\mathrm{\pi }}{3200}$ radian.
 A circle is defined as $2\mathrm{Pi}$ radians.
 A semicircle is defined as $\mathrm{\pi }$ radians.
 A quadrant is defined as $\frac{\mathrm{\pi }}{2}$ radians.
 A sign is defined as $\frac{\mathrm{\pi }}{6}$ radian.
 A point is defined as $\frac{\mathrm{\pi }}{16}$ radian.
 An hour is defined as $\frac{\mathrm{\pi }}{12}$ radian.

Examples

 > $\mathrm{convert}\left('\mathrm{radian}','\mathrm{dimensions}'\right)$
 ${\mathrm{plane_angle}}$ (1)
 > $\mathrm{convert}\left('\mathrm{radian}','\mathrm{dimensions}','\mathrm{base}'=\mathrm{true}\right)$
 $\frac{{\mathrm{length}}}{{\mathrm{length}}{}\left({\mathrm{radius}}\right)}$ (2)
 > $\mathrm{convert}\left(10,'\mathrm{units}','\mathrm{degrees}','\mathrm{radians}'\right)$
 $\frac{{\mathrm{\pi }}}{{18}}$ (3)