Question

find the period and graph the function.

$y=-\cot x$

period = rad

Explanation:

Step1: Recall the period formula for cotangent function

The general form of a cotangent function is \(y = A\cot(Bx - C)+D\). The period of the cotangent function \(y=\cot(Bx)\) is given by the formula \(T=\frac{\pi}{|B|}\).

Step2: Identify the value of \(B\) in the given function

For the function \(y =-\cot(x)\), we can rewrite it as \(y=-\cot(1x)\). Here, \(B = 1\).

Step3: Calculate the period

Substitute \(B = 1\) into the period formula \(T=\frac{\pi}{|B|}\). So, \(T=\frac{\pi}{|1|}=\pi\).

Answer:

\(\pi\)