 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/14/c/solution

The original PDF specifies slope

3

; the transcription's

- 1

is erroneous. By part (a),

cot (t /2) = 3

. Since

t /2 \in (0, π)

and cotangent is strictly decreasing there, the unique parameter value is

t = π /3

. Therefore

(x, y) = (a (\frac{π}{3} - \frac{3}{2}), \frac{a}{2}) .

The tangent line drawn in the preceding figure has the required positive slope.

 New to topics? Read the docs here!