Difference between revisions of "Tangent Command"

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<noinclude>{{Manual Page}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
; Tangent[Point, Conic]: Creates (all) tangents through the point to the conic section.  
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; Tangent( <Point>, <Conic> )
; Tangent[Line, Conic]: Creates (all) tangents to the conic section that are parallel to the given line.
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: Creates (all) tangents through the point to the conic section.  
; Tangent[Number a, Function]: Creates the tangent to the function at ''x = a''.  
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:{{example|1=<code><nowiki>Tangent((5, 4), 4x^2 - 5y^2 = 20)</nowiki></code> yields ''x - y = 1''.}}
; Tangent[Point A, Function]: Creates the tangent to the function at ''x = x(A)''.
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; Tangent( <Point>, <Function> )
: Note: ''x(A)'' is the ''x''-coordinate of point ''A''.
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: Creates the tangent to the function at ''x = x(A)''.
; Tangent[Point, Curve]: Creates the tangent to the curve in the given point.
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: {{Note| ''x(A)'' is the ''x''-coordinate of the given point ''A''.}}
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:{{example|1=<code><nowiki>Tangent((1, 0), x^2)</nowiki></code> yields ''y = 2x - 1''.}}
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; Tangent( <Point on Curve>, <Curve> )
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: Creates the tangent to the curve in the given point.
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:{{example|1=<code><nowiki>Tangent((0, 1), Curve(cos(t), sin(t), t, 0, π))</nowiki></code> yields ''y = 1''.}}
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; Tangent( <x-Value>, <Function> )
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: Creates the tangent to the function at ''x-Value''.
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:{{example|1=<code><nowiki>Tangent(1, x^2)</nowiki></code> yields ''y = 2x - 1''.}}
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; Tangent( <Line>, <Conic> )
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: Creates (all) tangents to the conic section that are parallel to the given line.
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:{{example|1=<code><nowiki>Tangent(y = 4, x^2 + y^2 = 4)</nowiki></code> yields ''y = 2'' and ''y = -2''.}}
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; Tangent( <Circle>, <Circle> )
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: Creates the common tangents to the two Circles (up to 4).
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:{{example|1=<code><nowiki>Tangent(x^2 + y^2 = 4, (x - 6)^2 + y^2 = 4)</nowiki></code> yields ''y = 2'', ''y = -2'', ''1.49x + 1.67y = 4.47'' and ''-1.49x + 1.67y = -4.47''.}}
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;Tangent( <Point>, <Spline> )
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:Creates the tangent to the spline in the given point.
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:{{example|1=Let ''A = (0, 1)'', ''B = (4, 4)'' and ''C = (0, 4)''. <code><nowiki>Tangent(A, Spline({A, B, C}))</nowiki></code> yields line ''a'': ''y'' = ''0.59x + 1''.}}
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;Tangent( <Point>, <Implicit Curve> )
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:Creates the tangent to the implicit curve in the given point.
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:{{example|1=<code><nowiki>Tangent((1,1), x^2+y^2=1))</nowiki></code> yields lines ''x=1'' and ''y=1''.}}
  
'''Note:''' Also see tool [[Tangents Tool|Tangents]].
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{{Note| See also  [[File:Mode tangent.svg|link=|24px]] [[Tangents Tool|Tangents]] tool.}}

Latest revision as of 16:15, 6 March 2018


Tangent( <Point>, <Conic> )
Creates (all) tangents through the point to the conic section.
Example: Tangent((5, 4), 4x^2 - 5y^2 = 20) yields x - y = 1.
Tangent( <Point>, <Function> )
Creates the tangent to the function at x = x(A).
Note: x(A) is the x-coordinate of the given point A.
Example: Tangent((1, 0), x^2) yields y = 2x - 1.
Tangent( <Point on Curve>, <Curve> )
Creates the tangent to the curve in the given point.
Example: Tangent((0, 1), Curve(cos(t), sin(t), t, 0, π)) yields y = 1.
Tangent( <x-Value>, <Function> )
Creates the tangent to the function at x-Value.
Example: Tangent(1, x^2) yields y = 2x - 1.
Tangent( <Line>, <Conic> )
Creates (all) tangents to the conic section that are parallel to the given line.
Example: Tangent(y = 4, x^2 + y^2 = 4) yields y = 2 and y = -2.
Tangent( <Circle>, <Circle> )
Creates the common tangents to the two Circles (up to 4).
Example: Tangent(x^2 + y^2 = 4, (x - 6)^2 + y^2 = 4) yields y = 2, y = -2, 1.49x + 1.67y = 4.47 and -1.49x + 1.67y = -4.47.
Tangent( <Point>, <Spline> )
Creates the tangent to the spline in the given point.
Example: Let A = (0, 1), B = (4, 4) and C = (0, 4). Tangent(A, Spline({A, B, C})) yields line a: y = 0.59x + 1.
Tangent( <Point>, <Implicit Curve> )
Creates the tangent to the implicit curve in the given point.
Example: Tangent((1,1), x^2+y^2=1)) yields lines x=1 and y=1.


Note: See also Mode tangent.svg Tangents tool.
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