Standard coordinates on $\mathbb{R}^n$

Question

In book "An introduction to Manifolds (Tu Loring)" is written:

Let $(U,\phi)$ be a chart and $f$ a $C^{\infty}$ function on a Manifold $M$ of dimension $n$. As a function into $\mathbb{R}^n$, $\phi$ has $n$ components $x^1,…,x^n$. This means if $r^1…r^n$ are standard coordinates on $\mathbb{R}^n$, then $x^i = r^i \circ \phi$.

He considers $r ^ i $and $x ^ i$ as functions.What function $r^i$ is this?

Answer 1

I take it that $r^i:\Bbb R^n\to \Bbb R$ should be the projection onto the $i$-th coordinate.