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.)

Answer

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Answer

Final Answer: The algebraic expression in $u$ is $\boxed{\frac{1}{u}}$.

Steps

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 $\boxed{\frac{1}{u}}$.