Exercise on parametric curves

Question

The function $f:\left [ 0,4 \right ]\rightarrow \mathbb{R}^{2}$ whose rank is a square centered on the origin of coordinates and of side $2a$. It can be defined without using functions by sections?

Thanks for the help

Answer 1

You could use the curve

$$ f(t) = (\cos(t\pi/2)\cdot |\cos(t\pi/2)|,\:\: \sin(t\pi/2)\cdot|\sin(t\pi/2)|)$$

The image of this function is a square with side length $\sqrt{2}$, so you just have to scale the function accordingly to get a side length of $2a$.