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Graph the curve with parametric equations$$ x = (1 + \cos 16t) \cos t $$$$ y = (1 + \cos 16t) \sin t $$$$ z = 1 + \cos 16t $$Explain the appearance of the graph by showing that it lies on a cone.

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Plug the parametric equations into the cone equation $z^{2}=x^{2}+y^{2}$ to showthat the curve lies on it.

Calculus 3

Chapter 13

Vector Functions

Section 1

Vector Functions and Space Curves

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03:04

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"].

08:32

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.

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Graph the curve with param…

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Graph of the curve, with parametric equations x, equal to 1 plus cosine 16 t times cosine t y is equal to 1 plus cosine 16 t times sine t and t is equal to 1 last cosine 16 d explain the appearance of the graph by showing that It lost on a corn, so first by using some graphing device, can graph the curve as follows. So this is the curve of the given equations, which showed that in the last colonbaparametric equations x, y and c we have x, squared plus y square, is equal to 1 plus cosine 16 t square. But this is equal to z square and this is a corso. The curve lies on o.

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