# What is the cotangent of pi/2?

#### Understand the Problem

The question is asking for the value of the cotangent function at the angle pi/2 radians. Since cotangent is defined as the ratio of the cosine to the sine, we will need to evaluate this ratio at the specified angle.

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The value of cotangent at $\pi/2$ is undefined.

#### Steps to Solve

1. Evaluate sine and cosine at $\pi/2$ radians

At $\pi/2$ radians, the values of sine and cosine functions are:

$$\sin(\pi/2) = 1$$ $$\cos(\pi/2) = 0$$

1. Define cotangent function

The cotangent function is defined as the ratio of the cosine to the sine:

$$\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$$

1. Substitute the values into the cotangent function

Substitute $\pi/2$ into the cotangent function:

$$\cot(\pi/2) = \frac{\cos(\pi/2)}{\sin(\pi/2)} = \frac{0}{1}$$

1. Simplify the expression

Simplify the fraction:

$$\cot(\pi/2) = 0$$

However, since division by zero is undefined, it's important to recognize that the cotangent function has no defined value at this angle.

The correct notation is:

$$\cot(\pi/2) = \text{undefined}$$

The value of cotangent at $\pi/2$ is undefined.

The cotangent function is undefined where the sine function is zero because cotangent is the ratio of cosine to sine. At $\pi/2$ radians, sine is 1, and cosine is 0, leading to an undefined expression.