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Section 10.6 Vocabulary - Parametric Equations

                                    Name: ___________________
                                    Period: __________________
                                    Date: ____________________
Across
To determine the time when an object is at a given point (x, y) on a path, you can introduce a third variable t, called a(n) _________.
You still need the parametric equations to tell you the position, __________, and speed at a given time.
In applications, different parametric representations can be used to represent various ______ at which objects travel along a given path.
You still need the parametric equations to tell you the _________, direction, and speed at a given time.
It is not necessary for the parameter in a set of parametric equations to represent time. The next example uses a(n) _____ as the parameter.
You have been studying techniques for sketching the graph represented by a set of parametric equations. Now consider the ________ problem--that is, how can you find a set of parametric equations for a given graph of a given physical description?
Plotting the resulting points in the order of __________ values of t traces the curve in a specific motion.
When converting equations from parametric to rectangular form, you may need to _____ the domain of the rectangular equation so that its graph matches the graph of the parametric equations.
Note that the elliptical curve is traced out ________________ as θ increases on the interval [0, 2π).
A(n) ________ is a curve traced out by a point P on a circle as the circle rolls along a straight line in a plane.
The ____________ of the curve is the specific direction in the trace of a place curve.
___________ Motion: Two Variables for Position, One Variable for Time
In examples 2 and 3, it is important to realize that eliminating the parameter is primarily a(n) ___ to curve sketching.
Down
It is possible to write both x and y as functions of t to obtain the __________ equations.
Two different sets of parametric equations can have the ____ graph.
The curve represented by the parametric equations is shown in Figure 10.44. Note that the graphs in Figures 10.43 and 10.44 have ________ orientations.
To eliminate the parameter in equations involving trigonometric functions, try using ___________.
If f and g are continuous functions of t on an interval I, then the set of ordered pairs (f(t), g(t)) is a plane curve C. The _________ x = f(t) and y = g(t) are parametric _________ for C, and t is the parameter.
When _________ a curve represented by a pair of parametric equations, you still plot points in the xy-plane.
If f and g are continuous functions of t on an interval I, then the set of ordered pairs (f(t), g(t)) is a(n) _____ curve C.
Example 1 uses simple point plotting to sketch the curve. This tedious process can sometimes be simplified by finding a(n) ___________ equation (in x and y) that has the same graph.
Up to this point, you have been representing a graph by a single equation involving ___ variables such as x and y.
Parametric equations are useful for modeling the path of an object. For instance, in Exercise 95 on page 739, you will use a set of parametric equations to model the path of a(n) ________.
When using a value of t to find x, be sure to use the same value of t to find the _____________value of y. Organizing your results in a table, as shown in Example 1, can be helpful.
The process of finding a rectangular equation (in x and y) that has the same graph as a parametric equation is called ___________ the parameter.
In sketching a plane curve, each set of coordinates (x,y) is ___________ from a value chose for the parameter t.
One benefit of parametric equations is that they can be used to represent graphs that are more ______ than graphs of functions.
In this section, you will study situations in which it is useful to introduce a _____ variable to represent a curve in the plane.