The angle formed by the positive y-axis and the tangent to $\mathrm{y}={\mathrm{x}}^2+4\mathrm{x}-17\text{ at }(5/2,-3/4)$ is

$\begin{array}{l}\mathrm{y}={\mathrm{x}}^2+4\mathrm{x}-17\text{ or }\frac{\mathrm{dy}}{\mathrm{dx}}=2(\mathrm{x}+2)\text{ or }{\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{\mathrm{x}=\frac{5}{2}}=9\\ \mathrm{or} \tan \mathrm{\theta }=9\end{array}$

where $\theta$ is the angle with positive direction of x-axis.
Therefore, angle with y-axis it $\frac{\mathrm{\pi }}{2}\pm \mathrm{\theta }=\frac{\mathrm{\pi }}{2}\pm {\tan }^{-1}9$