8.5 Assessed Exercises 3

Solutions in tutor’s pigeonhole by 17:00 on Tuesday 6th December, please. Feedback is available from the moodle website.

A3.1. The curve $x=at-a\sin t$ and $y=a-a\cos t$ where $t\geq 0$ is a cycloid; this represents the motion of a point on the rim of a rotating wheel.

(i) Show that

(ii) Show that the length along the curve from the point $(x(0),y(0))=(0,0)$ to the point $(x(\pi),y(\pi))=(a\pi,2a)$ is $4a$.

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A3.2 Find and classify the stationary points of the function given by

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