Difference between revisions of "Sector Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
; Sector[ <Conic>, <Point>, <Point> ]
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; Sector( <Conic>, <Point>, <Point> )
 
:Yields a conic sector between two points on the conic section and calculates its area.
 
:Yields a conic sector between two points on the conic section and calculates its area.
 
:{{examples|1=<div>
 
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;Sector[ <Conic>, <Parameter Value>, <Parameter Value> ]
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;Sector( <Conic>, <Parameter Value>, <Parameter Value> )
 
:Yields a conic sector between two parameter values between ''0'' and ''2π'' on the conic section and calculates its area.
 
:Yields a conic sector between two parameter values between ''0'' and ''2π'' on the conic section and calculates its area.
 
:{{example|1=<div> Let <code><nowiki>c: x^2 + y^2 = 9</nowiki></code> be a circle. <code><nowiki>Sector[ c, 0, 3/4 π ]</nowiki></code> yields ''d = 10.6''</div>}}
 
:{{example|1=<div> Let <code><nowiki>c: x^2 + y^2 = 9</nowiki></code> be a circle. <code><nowiki>Sector[ c, 0, 3/4 π ]</nowiki></code> yields ''d = 10.6''</div>}}

Revision as of 17:17, 7 October 2017


Sector( <Conic>, <Point>, <Point> )
Yields a conic sector between two points on the conic section and calculates its area.
Examples:
  • Let c: x^2 + 2y^2 = 8 be an ellipse, D = (-2.83, 0) and E = (0, -2) two points on the ellipse. Sector[ c, D, E ] yields d = 4.44.
  • Let c: x^2 + y^2 = 9 be a circle, A = (3, 0) and B = (0, 3) two points on the circle. Sector[ c, A, B ] yields d = 7.07
Note: This works only for a circle or ellipse.


Sector( <Conic>, <Parameter Value>, <Parameter Value> )
Yields a conic sector between two parameter values between 0 and on the conic section and calculates its area.
Example:
Let c: x^2 + y^2 = 9 be a circle. Sector[ c, 0, 3/4 π ] yields d = 10.6
Note: Internally the following parametric forms are used:
  • Circle: (r cos(t), r sin(t)) where r is the circle's radius.
  • Ellipse: (a cos(t), b sin(t)) where a and b are the lengths of the semimajor and semiminor axes.
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