# Difference between revisions of "Sector Command"

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− | <noinclude>{{Manual Page | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} |

− | {{command|geometry}} | + | ; Sector( <Conic>, <Point>, <Point> ) |

− | ; Sector | + | :Yields a conic sector between two points on the conic section and calculates its area. |

− | : Note | + | :{{examples|1=<div> |

− | ; Sector | + | :* 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''. |

− | : Note | + | :* 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>}} |

− | :* Circle: ''(r cos(t), r sin(t))'' where ''r'' is the circle's radius. | + | :{{Note|1=This works only for a circle or ellipse.}} |

− | :* Ellipse: ''(a cos(t), b sin(t))'' where ''a'' and ''b'' are the lengths of the semimajor and semiminor axes. | + | |

+ | |||

+ | |||

+ | ;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. | ||

+ | :{{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: | ||

+ | :*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.}} |

## Latest revision as of 10:40, 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*

- Let

**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*2π*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.

- Circle: