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Download as PDF; Printable version; In other projects ... Arc length is the distance between two points ... To justify this formula, define the arc length as limit of ...
In geometry, the sagitta (sometimes abbreviated as sag [1]) of a circular arc is the distance from the midpoint of the arc to the midpoint of its chord. [2] It is used extensively in architecture when calculating the arc necessary to span a certain height and distance and also in optics where it is used to find the depth of a spherical mirror ...
The arc length, from the familiar geometry of a circle, is = The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of ):
A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...
The minor sector is shaded in green while the major sector is shaded white. A circular sector, also known as circle sector or disk sector or simply a sector (symbol: โ), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the minor sector and the larger being the major sector. [1]
This is analogous to the way circular angle measure is the arc length of an arc of the unit circle in the Euclidean plane or twice the area of the corresponding circular sector. Alternately hyperbolic angle is the area of a sector of the hyperbola = Some authors call the inverse hyperbolic functions hyperbolic area functions.
Using radians, the formula for the arc length s of a circular arc of radius r and subtending a central angle of measure ๐ is =, and the formula for the area A of a circular sector of radius r and with central angle of measure ๐ is A = 1 2 θ r 2 . {\displaystyle A={\frac {1}{2}}\theta r^{2}.}
The arc length of one branch between x = x 1 and x = x 2 is a ln โ y 1 / y 2 โ . The area between the tractrix and its asymptote is โ π a 2 / 2 โ , which can be found using integration or Mamikon's theorem .
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