= Solution
Matching the two <parametric equations> at an intersection gives $\cos\phi=-t$ and $\sin\phi=1+t$. The <Pythagorean trigonometric identity> therefore requires
$$
t^2+(1+t)^2=1,\qquad2t(t+1)=0.
$$
For $t=0$, the <sine> is one and the <cosine> is zero; for $t=-1$, the <cosine> is one and the <sine> is zero. Keeping the stated half-open angular interval gives
$$
\boxed{(t,\phi)=(0,\pi/2)\quad\text{or}\quad(-1,0).}
$$
The corresponding points are $(0,1)$ and $(2,0)$; both satisfy the original <parametric equations>.
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