question find the equation of the vertical asymptotes of the trigonometric function below in general form…

question find the equation of the vertical asymptotes of the trigonometric function below in general form (for all real values of x). express your answers as a single equation in terms of k, as determined by the dropdown below. f(x)=4cot(1/2πx) answer attempt 1 out of 2 equation: where k is an integer where k is a whole number where k is a rational number where k is a real number

question find the equation of the vertical asymptotes of the trigonometric function below in general form (for all real values of x). express your answers as a single equation in terms of k, as determined by the dropdown below. f(x)=4cot(1/2πx) answer attempt 1 out of 2 equation: where k is an integer where k is a whole number where k is a rational number where k is a real number

Answer

Explanation:

Step1: Recall cotangent asymptote property

The cotangent function $y = \cot(t)$ has vertical asymptotes when $t = k\pi$, where $k$ is an integer.

Step2: Set the argument of the cotangent equal to $k\pi$

For $y = 4\cot(\frac{1}{2}\pi x)$, set $\frac{1}{2}\pi x=k\pi$.

Step3: Solve for $x$

Divide both sides of $\frac{1}{2}\pi x = k\pi$ by $\frac{1}{2}\pi$. We get $x = 2k$.

Answer:

$x = 2k$, where $k$ is an integer