Express the ratios $\cos A$,$\tan A$,and $\sec A$ in terms of $\sin A$.

(N/A) We know the fundamental trigonometric identity: $\cos^2 A + \sin^2 A = 1$.
$1$. To express $\cos A$ in terms of $\sin A$:
$\cos^2 A = 1 - \sin^2 A$
$\cos A = \sqrt{1 - \sin^2 A}$ (taking the positive root for acute angle $A$)
$2$. To express $\tan A$ in terms of $\sin A$:
$\tan A = \frac{\sin A}{\cos A}$
Substituting the value of $\cos A$:
$\tan A = \frac{\sin A}{\sqrt{1 - \sin^2 A}}$
$3$. To express $\sec A$ in terms of $\sin A$:
$\sec A = \frac{1}{\cos A}$
Substituting the value of $\cos A$:
$\sec A = \frac{1}{\sqrt{1 - \sin^2 A}}$