Describe the following curve:
r(t)=2cost i +3sint j
The ans is:
An Ellipse
since (x^2)/(2^2)+(y^2)/(3^2) = 1
I cant see where they get this ans from?
$\displaystyle \displaystyle x = 2\cos{t} \implies \cos{t} = \frac{x}{2}$
$\displaystyle \displaystyle y = 3\sin{t} \implies \sin{t} = \frac{y}{3}$.
$\displaystyle \displaystyle \sin^2{t} + \cos^2{t} = 1$
$\displaystyle \displaystyle \left(\frac{y}{3}\right)^2 + \left(\frac{x}{2}\right)^2 = 1$
$\displaystyle \displaystyle \frac{y^2}{9} + \frac{x^2}{4} = 1$.
It's an ellipse.