What Is the Value of Cot (pi)?

By Staff WriterLast Updated Mar 27, 2020 5:37:50 AM ET

The value of cot(pi) is undefined. As x approaches pi from below, cot(x) tends towards negative infinity. However, as x approaches pi from above, cot(x) tends towards positive infinity.

The cotangent function, cot(x), is defined as 1/tan(x). Since tan(pi) = 0, cot(pi) is undefined. As one can see by looking at a graph of y = cot(x) against x, x = pi is a vertical asymptote of the function. These asymptotes appear at all multiples of x = pi, including x = -pi, 0, pi, 2pi, etc. The positions of these asymptotes correspond to the values of x at which tan(x) = 0.