Ans: Understanding Direction of a Parametric Equation

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To determine the direction of a parametric equation, one must analyze the behavior of both x and y values as the parameter t changes. In the provided example, the parametric equations x=2cos(t) and y=2sin(t) describe a circle with a radius of 2, not 4. The direction of the curve can be assessed by evaluating the values of t; as t increases from 0, the curve travels counterclockwise around the circle. Understanding whether x or y values are increasing helps clarify the direction of movement along the curve. Properly plotting points will reveal the trajectory of the curve based on the parameter t.
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Generally with parametric equations to determine the direction that the line or curve is traveling in, how can you be sure as to what direction it goes in? When you plot points, how do you know if its going from the left or to the right increasing, are they asking if the x values are increasing, or are they asking if what you get out of the function is increasing in order to determine what direction it's traveling in? -----ALSO----

Is this right?
Question is: graph the parametric equation: x=2cost , y=2sint

steps:
x/2 = cost
sint=y/2

the graph is a circle of radius 4 correct?

If done properly what direction will the curve be traveling in?
 
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Radius =2.
Give values to t, starting from 0 and see how the curve goes.
 

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