Difference between revisions of "Sector Command"

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; Sector( <Conic>, <Point>, <Point> )
; Sector[ <Conic>, <Point A>, <Point B> ]: Yields a conic sector between two points ''A'' and ''B'' on the conic section.
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:Yields a conic sector between two points on the conic section and calculates its area.
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:{{examples|1=<div>
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:* 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''.
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:* 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>, <Number t1>, <Number t2> ]: Yields a conic sector between two parameter values ''t1'' and ''t2'' on the conic section.
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;Sector( <Conic>, <Parameter Value>, <Parameter Value> )
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:Yields a conic sector between two parameter values between ''0'' and '''' on the conic section and calculates its area.
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:{{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.
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