Solve the equation for x, where x is restricted to the given interval.
-$y = 3 \tan 2 x - 1$, for $x$ in $\left( - \frac { \pi } { 4 } , \frac { \pi } { 4 } \right)$
A) $x = \frac { 1 } { 2 } \arctan \frac { y + 1 } { 3 }$
B) $x = 2 \arctan \frac { y + 1 } { 3 }$
C) $x = \frac { 1 } { 2 } \arctan ( 3 y + 3 )$
D) $x = 2 \arctan ( 3 y + 3 )$

Question

Quizplus · Accepted Answer

To solve for $x$, first isolate the trigonometric function: $3 \tan 2x = y + 1$. Then, divide by 3: $\tan 2x = \frac{y + 1}{3}$. Finally, apply the arctan function and solve for $x$: $2x = \arctan \frac{y + 1}{3}$, leading to $x = \frac{1}{2} \arctan \frac{y + 1}{3}$.

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