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Graph the curve with parametric equations $ x = \sin t $, $ y = \sin 2t $, $ z = \cos 4t $. Explain its shape by graphing its projections onto the three coordinate planes.

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Calculus 3

Chapter 13

Vector Functions

Section 1

Vector Functions and Space Curves

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University of Nottingham

Lectures

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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03:31

The problem is grape curve was parametric equations x, equal to sine t y is equal to sine 2 t. Z is equal to cosine 2 porte, explain its shape a graphing, its projections out to the 3 coordinate plies. So, first, by using some graphing device, we can graph the curve as follows. So this is the curve of the given parametric equations. Now the projection of x y plane, the graph is like a figure 8, the projection on axtellikea, wtheprojuction and isa. This is a problem.

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