Cartesian equation.

Murphie · #1 $Old$ August 9th, 2009, 07:22 PM

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.

skeeter · #2 $Old$ August 9th, 2009, 07:35 PM

Quote:

Originally Posted by Murphie $View Post$

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

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

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