Difference between revisions of "Sector Command"

From GeoGebra Manual
Jump to: navigation, search
(command syntax: changed [ ] into ( ))
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
; Sector[ <Conic>, <Point>, <Point> ]
+
; 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>
 
:{{examples|1=<div>
:* Let <code><nowiki>c: x^2 + 2y^2 = 8</nowiki></code> be an ellipse, <code><nowiki>D = (-2.83, 0)</nowiki></code> and <code><nowiki>E = (0, -2)</nowiki></code> two points on the ellipse. <code><nowiki>Sector[ c, D, E ]</nowiki></code> yields ''d = 4.44''.
+
:* Let <code><nowiki>c: x^2 + 2y^2 = 8</nowiki></code> be an ellipse, <code><nowiki>D = (-2.83, 0)</nowiki></code> and <code><nowiki>E = (0, -2)</nowiki></code> two points on the ellipse. <code><nowiki>Sector(c, D, E)</nowiki></code> yields ''d = 4.44''.
:* Let <code><nowiki>c: x^2 + y^2 = 9</nowiki></code> be a circle, <code><nowiki>A = (3, 0)</nowiki></code> and <code><nowiki>B = (0, 3)</nowiki></code> two points on the circle. <code><nowiki>Sector[ c, A, B ]</nowiki></code> yields ''d = 7.07''</div>}}
+
:* Let <code><nowiki>c: x^2 + y^2 = 9</nowiki></code> be a circle, <code><nowiki>A = (3, 0)</nowiki></code> and <code><nowiki>B = (0, 3)</nowiki></code> two points on the circle. <code><nowiki>Sector(c, A, B)</nowiki></code> yields ''d = 7.07''</div>}}
 
:{{Note|1=This works only for a circle or ellipse.}}
 
:{{Note|1=This works only for a circle or ellipse.}}
  
  
  
;Sector[ <Conic>, <Parameter Value>, <Parameter Value> ]
+
;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= 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''}}
 
:{{Note|1=Internally the following parametric forms are used:  
 
:{{Note|1=Internally the following parametric forms are used:  
 
:*Circle: ''(r cos(t), r sin(t))'' where ''r'' is the circle's radius.  
 
:*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.}}
 
:*Ellipse: ''(a cos(t), b sin(t))'' where ''a'' and ''b'' are the lengths of the semimajor and semiminor axes.}}

Latest revision as of 09:40, 11 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.
© 2021 International GeoGebra Institute