Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 173: 57

The least positive number for which $y = cot~x$ is undefined is $x = \pi$

We can find the least positive number for which $y = cot~x$ is undefined: $cot~x = \frac{cos~x}{sin~x}$ $cot~x$ is undefined when $sin~x = 0$. The least positive number for which $sin~x = 0$ is $x = \pi$ The least positive number for which $y = cot~x$ is undefined is $x = \pi$