Some doubts about an exercise from the famous book "Schaum's Outline of Differential Geometry"

Some doubts about an exercise from the famous book "Schaum's Outline of Differential Geometry":

Show that the rappresentation
x(t)=1+cos(t), y(t)=sin(t) z=2*sin(t/2) for t in [-2 pi, 2 pi]
is regular and lies on the sphere of radius 2 about the origin and the cylinder (x-1)²+y²=1

The rappresentation is regular, but the trend we found is not the same as that of the cited book.

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