Write the following as an algebraic expression in u, u 0.
-$\sin \left( \arcsin \frac { \mathrm { u } } { \sqrt { 3 } } \right)$
A) $\frac { \mathrm { u } \sqrt { 3 } } { 3 }$
B) $\frac { u \sqrt { u ^ { 2 } - 3 } } { u ^ { 2 } - 3 }$
C) $\frac { \sqrt { u ^ { 2 } + 3 } } { u ^ { 2 } + 3 }$
D) $\mathrm { u } \sqrt { 3 }$

Question

Write the following as an algebraic expression in u, u > 0.
-$\sin \left( \arcsin \frac { \mathrm { u } } { \sqrt { 3 } } \right)$
A) $\frac { \mathrm { u } \sqrt { 3 } } { 3 }$
B) $\frac { u \sqrt { u ^ { 2 } - 3 } } { u ^ { 2 } - 3 }$
C) $\frac { \sqrt { u ^ { 2 } + 3 } } { u ^ { 2 } + 3 }$
D) $\mathrm { u } \sqrt { 3 }$

Quizplus · Accepted Answer

The expression $\sin(\arcsin(\frac{u}{\sqrt{3}}))$ simplifies directly to $\frac{u}{\sqrt{3}}$ because the $\sin$ and $\arcsin$ functions are inverses of each other, canceling each other out. However, none of the given options exactly match this simplification. The correct choice, A, is a misinterpretation of the simplification process. The actual simplification should directly yield $\frac{u}{\sqrt{3}}$, but this is not an option provided. Therefore, it appears there has been a misunderstanding in interpreting the options relative to the simplification provided.

Write the Following as an Algebraic Expression in U, U sin⁡(arcsin⁡u3)\sin \left( \arcsin \frac { \mathrm { u } } { \sqrt { 3 } } \right)sin(arcsin3​u​)

Write the Following as an Algebraic Expression in U, U $\sin \left( \arcsin \frac { \mathrm { u } } { \sqrt { 3 } } \right)$