Write the trigonometric expression as an algebraic expression in $\mathrm{u}$. \[ \sin \left(\csc ^{-1} u\right) \] \[ \sin \left(\csc ^{-1} u\right)= \] (Type an exact answer, using radicals as needed.)

Step 1 ：The given expression is \(\sin (\csc ^{-1} u)\).

Step 2 ：Here, \(\csc ^{-1} u\) is the inverse cosecant function, which gives the angle whose cosecant is \(u\).

Step 3 ：The sine of this angle is then the reciprocal of \(u\), because sine and cosecant are reciprocal trigonometric functions.

Step 4 ：Therefore, the algebraic expression in \(u\) is \(\frac{1}{u}\).

Step 5 ：Final Answer: The algebraic expression in \(u\) is \(\boxed{\frac{1}{u}}\).