 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/13/b/i/solution

Substituting the endpoint parameter values gives

r (0) = (1, 0, 0), r (π /12) = (0, 1, 2 π /3) .

The curve lies on the unit circular cylinder

x^{2} + y^{2} = 1

. Its azimuth increases from zero to

π /2

while its height increases linearly, so it is one quarter-turn of a rising helix. The arrow in the sketch indicates increasing parameter.

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