The curve $C$ is defined parametrically by

for $-\pi <t<\pi .$

The curve is bound by a rectangle whose sides lie tangent to $C$ and parallel to the axes.

Find the area of the rectangle.

Focus on finding the largest and smallest possible values of $y=t^2-4$. You might even find it most convenient to plot the curve $y=t^2-4$ with the horizontal axis as $t$ and the vertical axis as $y$.

The smallest value of $y$ tells you the lowest point on the curve, and the largest value of $y$ tells you the highest.

To find the leftmost and rightmost points on the curve, you need to find the largest and smallest values of $x$. You can use $\frac{dx}{dt}=0$, or you can convert $x$ into harmonic form.

Give your answer to $3$ significant figures.