Solve the following equation.
$$\csc ^ { 2 } ( x ) - 4 = 0$$
A) $\frac { \pi } { 3 } + \pi n , \frac { 2 \pi } { 3 } + \pi n$, where $n$ is an integer
B) $\frac { \pi } { 3 } + 2 \pi n , \frac { 2 \pi } { 3 } + 2 \pi n$, where $n$ is an integer
C) $\frac { \pi } { 6 } + \pi n , \frac { 5 \pi } { 6 } + \pi n$, where $n$ is an integer
D) $\frac { \pi } { 6 } + 2 \pi n , \frac { 2 \pi } { 3 } + 2 \pi n$, where $n$ is an integer
E) $\frac { \pi } { 6 } + 2 \pi n , \frac { 5 \pi } { 6 } + 2 \pi n$, where $n$ is an integer

Question

Quizplus · Accepted Answer

The equation $\csc^2(x) - 4 = 0$ simplifies to $\csc^2(x) = 4$, which means $\csc(x) = \pm 2$. This implies $\sin(x) = \pm \frac{1}{2}$. The solutions for $\sin(x) = \frac{1}{2}$ are $x = \frac{\pi}{6} + 2\pi n$ and for $\sin(x) = -\frac{1}{2}$ are $x = \frac{5\pi}{6} + 2\pi n$, where $n$ is an integer.

Solve the Following Equation csc⁡2(x)−4=0\csc ^ { 2 } ( x ) - 4 = 0csc2(x)−4=0

Solve the Following Equation $\csc ^ { 2 } ( x ) - 4 = 0$