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Calculus/parametic equations

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Expert: - 3/19/2010


Question
Ok, I have this problem on my homework and I'm really stumped about it.

Consider the parametric equation x = 4 cos^2 t and y = 2 sin t.

a) Complete the table:

t | -pi/2 | -pi/4 | 0 | pi/4 | pi/2
x |       |       |   |      |
y |       |       |   |      |

Ovbiously I'm supposed to find the x and y values. Here's what I came up with:

t | -pi/2 | -pi/4 | 0 | pi/4 | pi/2
x |   0   |   2   | 4 |  2   |  0
y |  -2   |  -1.4 | 0 |  1.4 |  2

Are these correct?

Because for part b I'm supposed to plot the points on a graph and show the graph of the parametric equation, but I am at a loss for how to do this because the program I have refuses to form the curve for it. The graphing is the main part I need assistance with.

Thanks very much :)

-Gabe

Answer
Yes, there are correct.
To graph it, take a sheet of graph paper and count each space as a tenth.
Mark the origin in the center of the graph paper.

Make a horizontal line through the origin and call it the x axis.
Make a vertical line through the origin and call it the y axis.

Find the x value on the x axis and the y value on the y axis.
The point to plot is straight above he point found on the x axis and
straigh over from the point on the y axis.

The should form something that looks like a hyperbola with a vertical line through the origin.

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