Find an algebraic expression equivalent to the given expression.
-$\sin ( \arctan u )$
A) $\frac { \sqrt { \mathrm { u } ^ { 2 } - 1 } } { \mathrm { u } }$
B) $\frac { \mathrm { u } \sqrt { \mathrm { u } ^ { 2 } + 1 } } { \mathrm { u } ^ { 2 } + 1 }$
C) $\sqrt { u ^ { 2 } + 1 }$
D) $\sqrt { \mathrm { u } ^ { 2 } - 1 }$

Question

Quizplus · Accepted Answer

To find $\sin(\arctan(u))$, consider a right triangle where $u = \frac{\text{opposite}}{\text{adjacent}}$. Using the Pythagorean theorem, the hypotenuse is $\sqrt{u^2 + 1}$. Thus, $\sin(\arctan(u)) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{u}{\sqrt{u^2 + 1}}$, which simplifies to option B.

Find an Algebraic Expression Equivalent to the Given Expression sin⁡(arctan⁡u)\sin ( \arctan u )sin(arctanu)

Find an Algebraic Expression Equivalent to the Given Expression $\sin ( \arctan u )$