Given that $\theta$ is acute and $\sin \theta = s$, express, in terms of $s$,

1. Find an expression for $\cos \theta$ in terms of $s$.

Since $\sin^2 \theta + \cos^2 \theta = 1$, we have $\cos^2 \theta = 1 - s^2$.
Given that $\theta$ is acute, $\cos \theta > 0$, so $\cos \theta = \sqrt{1 - s^2}$.

2. Express $\tan \theta$ in terms of $s$.

$\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{s}{\sqrt{1 - s^2}}$

1. Express $\sec \theta$ in terms of $\cos \theta$

$\sec \theta = \frac{1}{\cos \theta}$

2. Substitute $\cos \theta$ in terms of $s$

Since $\sin \theta = s$ and $\theta$ is acute, $\cos \theta = \sqrt{1 - \sin^2 \theta} = \sqrt{1 - s^2}$.

$\sec \theta = \frac{1}{\sqrt{1 - s^2}}$