# Cartesian equation.

• Aug 9th 2009, 06:22 PM
Murphie
Cartesian equation.
Would someone mind telling me how to find the indicated direction in the problem below? Help with (b) would also be greatly appreciated!

(a) Graph the parametrized curve described by x = 2 cos t, y = -sin t, 0≤t≤pi. Indicate the direction in which the curve is traced.

(b) Find a Cartesian equation for the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve?

Thanks.
• Aug 9th 2009, 06:35 PM
skeeter
Quote:

Originally Posted by Murphie
Would someone mind telling me how to find the indicated direction in the problem below? Help with (b) would also be greatly appreciated!

(a) Graph the parametrized curve described by x = 2 cos t, y = -sin t, 0≤t≤pi. Indicate the direction in which the curve is traced.

(b) Find a Cartesian equation for the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve?

Thanks.

(a) traces clockwise from (2,0) to (-2,0) ... bottom half of an ellipse.

(b) $x^2 = 4\cos^2{t}$ ... $\cos^2{t} = \frac{x^2}{4}$

$y^2 = \sin^2{t} = 1 - \cos^2{t} = 1 - \frac{x^2}{4}$

$y = -\sqrt{1 - \frac{x^2}{4}}
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