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.

Figure 1.
Quarter-turn helix with its endpoints and projection onto the horizontal plane
. Details.

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