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> ] | ; Sector[ <Conic>, <Point>, <Point> ] | ||
− | :Yields a conic sector between two points on the conic section. | + | :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 + 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>}} | ||
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;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. | + | :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>}} | ||
:{{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.}} |
Revision as of 17:40, 9 October 2015
- 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)
andE = (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)
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 = 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.