The following line creates the curve of the unit tangent vector-valued function. (Invisible by Default). Upon activating the visibility, notice how it is never anything more than the arcs of a circle with radius 1.
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less than or equal to "t" less than or equal to
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The following line creates a point traveling along the curve of the unit tangent vector-valued function. (Invisible by default). Upon activating the visibility, notice how the point acts like a compass pointing in the direction of the point on the velocity vector-valued function
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equals
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The following two lines simulate the unit tangent vector placed on top of the point moving along the curve. This is done by creating a line with certain restrictions on its domain. Notice how the vector always points towards the concavity of the graph.
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The following two lines create the curve and a point on the curve of the principal unit normal vector-valued function. (Invisible by default). Upon activating the visibility, notice how it acts like another compass pointing in a direction perpendicular to that of the unit tangent "compass"
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less than or equal to "t" less than or equal to
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equals
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For the sake of better visibility, the following two lines recreate the principal normal unit vector-valued function with a reduced size so that it is distinguishable from the unit tangent vector-valued function. (Invisible by default). It is recommended to activate the visibility of the following two instead of the previous two lines.
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less than or equal to "t" less than or equal to
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equals
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The following two lines simulate the principal unit normal vector placed on top of the point moving along the curve. This is done by creating a line with certain restrictions on its domain.
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The following lines of code are not graphically representative of anything useful, but are vital to the calculations of the utility, so they should not be deleted. They are invisibly by default, but activating visibility demonstrates the complexity that this process can reach with manual calculations.
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less than or equal to "t" less than or equal to
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equals
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*Despite various attempts, a bug persists where vertical vectors are not shown (because the "slope" is undefined). However, since it is rare to find a graph with an undefined slope for longer than an instance, this bug is not at all noticeable when the slider is turned on.
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Utility created by Andres Holguin
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powered by
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Examples
Lines: Slope Intercept Form
example
Lines: Point Slope Form
example
Lines: Two Point Form
example
Parabolas: Standard Form
example
Parabolas: Vertex Form
example
Parabolas: Standard Form + Tangent
example
Trigonometry: Period and Amplitude
example
Trigonometry: Phase
example
Trigonometry: Wave Interference
example
Trigonometry: Unit Circle
example
Conic Sections: Circle
example
Conic Sections: Parabola and Focus
example
Conic Sections: Ellipse with Foci
example
Conic Sections: Hyperbola
example
Polar: Rose
example
Polar: Logarithmic Spiral
example
Polar: Limacon
example
Polar: Conic Sections
example
Parametric: Introduction
example
Parametric: Cycloid
example
Transformations: Translating a Function
example
Transformations: Scaling a Function
example
Transformations: Inverse of a Function
example
Statistics: Linear Regression
example
Statistics: Anscombe's Quartet
example
Statistics: 4th Order Polynomial
example
Lists: Family of sin Curves
example
Lists: Curve Stitching
example
Lists: Plotting a List of Points
example
Calculus: Derivatives
example
Calculus: Secant Line
example
Calculus: Tangent Line
example
Calculus: Taylor Expansion of sin(x)
example
Calculus: Integrals
example
Calculus: Integral with adjustable bounds
example
Calculus: Fundamental Theorem of Calculus
example
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