find the period. y = -cot(x)

Explanation:

Step1: Recall cotangent period formula

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

Step2: Identify the value of B

For the function $y =-\cot(x)$, we can rewrite it as $y=-1\times\cot(1\times x - 0)+0$. Here, $B = 1$.

Step3: Calculate the period

Substitute $B = 1$ into the period formula $T=\frac{\pi}{|B|}$. We get $T=\frac{\pi}{|1|}=\pi$.

Answer:

$\pi$