Find the exact solution of the equation.
-$$- \sin ^ { - 1 } ( 4 x ) = \frac { \pi } { 4 }$$
A) $x = - \frac { \sqrt { 2 } } { 8 }$
B) $x = \frac { \sqrt { 2 } } { 8 }$
C) $x = - \frac { \sqrt { 2 } } { 2 }$
D) $x = 0$

Question

Quizplus · Accepted Answer

To solve the equation $- \sin ^ { - 1 } ( 4 x ) = \frac { \pi } { 4 }$, we first get rid of the negative sign on the left side by multiplying both sides by -1, giving us $\sin ^ { - 1 } ( 4 x ) = -\frac { \pi } { 4 }$. The sine of an angle that gives $-\frac { \pi } { 4 }$ is $-\frac{\sqrt{2}}{2}$, so we have $4x = -\frac{\sqrt{2}}{2}$. Solving for $x$ gives $x = -\frac{\sqrt{2}}{8}$.

Find the Exact Solution of the Equation −sin⁡−1(4x)=π4- \sin ^ { - 1 } ( 4 x ) = \frac { \pi } { 4 }−sin−1(4x)=4π​

Find the Exact Solution of the Equation $- \sin ^ { - 1 } ( 4 x ) = \frac { \pi } { 4 }$