Difference between revisions of "Tangent Command"
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− | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} |
− | {{command|geometry}} | + | ; Tangent( <Point>, <Conic> ) |
− | ; Tangent | + | : Creates (all) tangents through the point to the conic section. |
− | + | :{{example|1=<code><nowiki>Tangent((5, 4), 4x^2 - 5y^2 = 20)</nowiki></code> yields ''x - y = 1''.}} | |
− | + | ; Tangent( <Point>, <Function> ) | |
− | + | : Creates the tangent to the function at ''x = x(A)''. | |
− | ; Tangent | + | : {{Note| ''x(A)'' is the ''x''-coordinate of the given point ''A''.}} |
− | : {{Note| ''x(A)'' is the ''x''-coordinate of point ''A''.}} | + | :{{example|1=<code><nowiki>Tangent((1, 0), x^2)</nowiki></code> yields ''y = 2x - 1''.}} |
− | ; Tangent | + | ; Tangent( <Point on Curve>, <Curve> ) |
− | ; Tangent | + | : Creates the tangent to the curve in the given point. |
− | ; Tangent | + | :{{example|1=<code><nowiki>Tangent((0, 1), Curve(cos(t), sin(t), t, 0, π))</nowiki></code> yields ''y = 1''.}} |
− | {{Note| See also [[Tangents Tool|Tangents]] tool.}} | + | ; Tangent( <x-Value>, <Function> ) |
+ | : Creates the tangent to the function at ''x-Value''. | ||
+ | :{{example|1=<code><nowiki>Tangent(1, x^2)</nowiki></code> yields ''y = 2x - 1''.}} | ||
+ | ; Tangent( <Line>, <Conic> ) | ||
+ | : Creates (all) tangents to the conic section that are parallel to the given line. | ||
+ | :{{example|1=<code><nowiki>Tangent(y = 4, x^2 + y^2 = 4)</nowiki></code> yields ''y = 2'' and ''y = -2''.}} | ||
+ | ; Tangent( <Circle>, <Circle> ) | ||
+ | : Creates the common tangents to the two Circles (up to 4). | ||
+ | :{{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''.}} | ||
+ | ;Tangent( <Point>, <Spline> ) | ||
+ | :Creates the tangent to the spline in the given point. | ||
+ | :{{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''.}} | ||
+ | ;Tangent( <Point>, <Implicit Curve> ) | ||
+ | :Creates the tangent to the implicit curve in the given point. | ||
+ | :{{example|1=<code><nowiki>Tangent((1,1), x^2+y^2=1))</nowiki></code> yields lines ''x=1'' and ''y=1''.}} | ||
+ | |||
+ | {{Note| See also [[File:Mode tangent.svg|link=|24px]] [[Tangents Tool|Tangents]] tool.}} |
Latest revision as of 17:15, 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 Tangents tool.