Difference between revisions of "Sector Command"
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| − | <noinclude>{{Manual Page|version= | + | <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. |
| + | :{{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 + 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 | + | |
| + | |||
| + | ;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: | :{{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 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 = 8be an ellipse,D = (-2.83, 0)andE = (0, -2)two points on the ellipse.Sector(c, D, E)yields d = 4.44. - Let
c: x^2 + y^2 = 9be a circle,A = (3, 0)andB = (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 = 9be 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.
