Solve the equation for x, where x is restricted to the given interval.
-$y = - 5 \sin 8 x$, for $x$ in $\left[ - \frac { \pi } { 16 } , \frac { \pi } { 16 } \right]$
A) $x = \frac { 1 } { 5 } \arcsin \left( - \frac { y } { 8 } \right)$
B) $x = - \frac { 1 } { 5 } \arcsin \frac { y } { 8 }$
C) $x = \frac { 1 } { 8 } \arcsin \left( - \frac { y } { 5 } \right)$
D) $x = \frac { 1 } { 8 } \arcsin \frac { y } { 5 }$

Question

Quizplus · Accepted Answer

To solve for $x$, we start with $y = -5\sin(8x)$. We want to isolate $x$, so we divide both sides by $-5$, giving $\frac{y}{-5} = \sin(8x)$, or $\sin(8x) = -\frac{y}{5}$. Taking the inverse sine of both sides gives $8x = \arcsin\left(-\frac{y}{5}\right)$. Finally, dividing both sides by 8 gives $x = \frac{1}{8}\arcsin\left(-\frac{y}{5}\right)$, which matches choice C.

Solve the Equation for X, Where X Is Restricted to the Given