Solve the equation for x, where x is restricted to the given interval.
-$y = 8 \cos 3 x$, for $x$ in $\left[ 0 , \frac { \pi } { 3 } \right]$
A) $x = 8 \arccos \frac { y } { 3 }$
B) $x = \frac { 1 } { 8 } \arccos \frac { y } { 3 }$
C) $x = 3 \arccos \frac { y } { 8 }$
D) $x = \frac { 1 } { 3 } \arccos \frac { y } { 8 }$

Question

Quizplus · Accepted Answer

To solve for $x$, we first isolate $x$ in the equation $y = 8 \cos 3x$. Dividing both sides by 8 gives $\cos 3x = \frac{y}{8}$. Then, applying the inverse cosine function to both sides gives $3x = \arccos \frac{y}{8}$. Finally, dividing both sides by 3 gives $x = \frac{1}{3} \arccos \frac{y}{8}$, which matches choice D.

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