select all that are asymptotes of the tangent graph.\n$x = \\frac{\\pi}{4}$\n$x = \\frac{\\pi}{2}$\n$x =…

select all that are asymptotes of the tangent graph.\n$x = \\frac{\\pi}{4}$\n$x = \\frac{\\pi}{2}$\n$x = \\pi$\n$x = \\frac{3\\pi}{2}$\n$x = 3\\pi$\ndone

select all that are asymptotes of the tangent graph.\n$x = \\frac{\\pi}{4}$\n$x = \\frac{\\pi}{2}$\n$x = \\pi$\n$x = \\frac{3\\pi}{2}$\n$x = 3\\pi$\ndone

Answer

Answer:

B. $x = \frac{\pi}{2}$, D. $x=\frac{3\pi}{2}$

Explanation:

Step1: Recall tangent function formula

$y = \tan(x)=\frac{\sin(x)}{\cos(x)}$

Step2: Find asymptote condition

Asymptotes occur when $\cos(x)=0$.

Step3: Solve $\cos(x) = 0$

The solutions of $\cos(x)=0$ are $x=\frac{\pi}{2}+k\pi$, where $k\in\mathbb{Z}$. When $k = 0$, $x=\frac{\pi}{2}$; when $k = 1$, $x=\frac{\pi}{2}+\pi=\frac{3\pi}{2}$. So $x=\frac{\pi}{2}$ and $x=\frac{3\pi}{2}$ are asymptotes of the tangent - graph.