 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1/10/b/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

d x / d t \neq = 0

, the chain rule gives

\frac{d y}{d x} = \frac{2 c o s t}{- s i n t} .

The specified point has

cos t = sin t = 1/ 2

, hence

t = π /4

in the given traversal. Therefore

\frac{d y}{d x} = - 2.

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