= Solution
Substituting the endpoint parameter values gives
$$
\boxed{\mathbf r(0)=(1,0,0),\qquad\mathbf r(\pi/12)=(0,1,2\pi/3).}
$$
The curve lies on the unit circular <cylinder> $x^2+y^2=1$. Its azimuth increases from zero to $\pi/2$ while its height increases linearly, so it is one quarter-turn of a rising <helix>. The arrow in the sketch indicates increasing parameter.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2-2018-q13-quarter-helix.png]
{title=Quarter-turn helix with its endpoints and projection onto the horizontal plane}
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