Freeflows

Parametric Curve Interval

A parametric curve is defined by \[(x,y) = (\sin^2 t, 2 \cos t),\]where $ t $ ranges over all real numbers. The same parametric curve can be defined by \[(x,y) = (-s^2 - 2s, 2s + 2),\]where $ s $ ranges over some interval $ I $. Find the interval $ I $.

1
2
3
+
4
5
6
-
7
8
9
$\frac{a}{b}$
.
0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$

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