Difference between revisions of "Tangent Command"
From GeoGebra Manual
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;Tangent[ <Point>, <Spline> ] | ;Tangent[ <Point>, <Spline> ] | ||
:Creates the tangent to the spline in the given point. | :Creates the tangent to the spline in the given point. | ||
− | :{{example|1=<div>Let ''A = (0, 1)'', ''B = (4, 4)'' and ''C = (0, 4)''. </div> <div><code><nowiki>Tangent[A, Spline[{A, B, C}]]</nowiki></code> yields line ''a'': ''y'' = ''0. | + | :{{example|1=<div>Let ''A = (0, 1)'', ''B = (4, 4)'' and ''C = (0, 4)''. </div> <div><code><nowiki>Tangent[A, Spline[{A, B, C}]]</nowiki></code> yields line ''a'': ''y'' = ''0.59x + 1''.</div>}} |
{{Note| See also [[File:Mode tangent.svg|link=|24px]] [[Tangents Tool|Tangents]] tool.}} | {{Note| See also [[File:Mode tangent.svg|link=|24px]] [[Tangents Tool|Tangents]] tool.}} |
Revision as of 22:52, 23 December 2015
- 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.
Note: See also Tangents tool.