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Sketch the curve with the given vector equation. Indicate with an arrow the direction in which $ t $ increases.
$ r(t) = \langle \sin \pi t , t , \cos \pi t \rangle $
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Vector Functions and Space Curves
Harvey Mudd College
University of Michigan - Ann Arbor
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.
Sketch the curve with the …
So what we're given is that our our position um, position vector is sign piety T Kherson Patty. So we know that the why values going to constantly increase, um and then the x n Z values are going to make a circular pattern, so it's gonna end up giving us a spiral shape, and it's going to look like this. So since this is our why right here, we wanted to be going in this direction. So we're going to end up having is something that looks like this continues on and on. We can use an increment of pi over six. Um, and if we just create a table of values, we can graph that. We see that the spiral goes and the positive y axis direction. So we see that it will go like this and then like this, like this so we can draw those arrows just to give in a sense of which direction it's moving. Um, and that's because we know that X equals co sign T and y equals Sign T gives us a circle. So if we have signed pity coastline, pity that's going to give us a circle and the tea is the Y values, so that's gonna just constantly increase as T increases
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