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Use a computer to graph the curve with the given vector equation. Make sure you choose a parameter domain and viewpoints that reveal the true nature of the curve.
$ r(t) = \langle \cos t \sin 2t, \sin t \sin 2t, \cos 2t \rangle $
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GeoGebra command:Curve $(\cos (t) \sin (2 t), \sin (t) \sin (2 t), \cos (2 t), t, 0,2$ pi)
Vector Functions and Space Curves
Harvey Mudd College
University of Michigan - Ann Arbor
University of Nottingham
In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x.
The input of a function is called the argument and the output is called the value. The set of all permitted inputs is called the domain of the function. Similarly, the set of all permissible outputs is called the codomain. The most common symbols used to represent functions in mathematics are f and g. The set of all possible values of a function is called the image of the function, while the set of all functions from a set "A" to a set "B" is called the set of "B"-valued functions or the function space "B"["A"].
In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.
Use a computer to graph th…
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The problem is use a computer to graph the curve where it's given vector equation, make sure you choose a parameter domain and whale points that reveal the true nature of the curve or t is equal to sine t sine 2 t sine t sine 2 t cosine 2 t pot i'm using some graphing device. We can graph the curve as follows. So here this is the curve of the given equation.
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