what is parametric and periodic function
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a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. ... Parameterizations are non-unique; more than one set of parametric equations can specify the same curve.
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When an object moves along a curve—or curvilinear path—in a given direction and in a given amount of time, the position of the object in the plane is given by the x-coordinate and the y-coordinate.
However, both\,x\,and\,y\,
vary over time and so are functions of time. For this reason, we add another variable, the parameter, upon which both\,x\,and\,y\,are dependent functions. In the example in the section opener, the parameter is time,\,t.\,The\,x\,position of the moon at time,\,t,\,is represented as the function\,x\left(t\right),\,and the\,y\,position
of the moon at time,\,t,\,is represented as the function\,y\left(t\right).\,Together,\,x\left(t\right)\, and \,y\left(t\right)\, are called parametric equations, and generate an ordered pair\,\left(x\left(t\right),\,y\left(t\right)\right).\,Parametric equations primarily describe motion and direction.
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