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

The original PDF specifies slope $\sqrt{3}$; the transcription's $\sqrt{-1}$ is erroneous. By part (a), $\cot (t/2)=\sqrt{3}$. Since $t/2\in (0,\pi )$ and cotangent is strictly decreasing there, the unique parameter value is $t=\pi /3$. ThereforeThe tangent line drawn in the preceding figure has the required positive slope.