which of the following is an asymptote of y = csc(x)?\no x = -π\no x = -\\frac{π}{3}\no x = \\frac{π}{4}\no…
which of the following is an asymptote of y = csc(x)?\no x = -π\no x = -\\frac{π}{3}\no x = \\frac{π}{4}\no x = \\frac{π}{2}
Answer
Explanation:
Step1: Recall the definition of cosecant
The cosecant function is defined as $\csc(x)=\frac{1}{\sin(x)}$. Asymptotes occur where the function is undefined, i.e., where $\sin(x) = 0$.
Step2: Find the zeros of sine function
The general solution for $\sin(x)=0$ is $x = k\pi$, where $k\in\mathbb{Z}$ (integers).
Step3: Check the options
When $k=- 1$, $x=-\pi$ and $\sin(-\pi)=0$. So $x =-\pi$ makes $\csc(x)$ undefined.
Answer:
$x =-\pi$