# What is the cot of 90 degrees?

#### Understand the Problem

The question is asking for the value of the cotangent (cot) of 90 degrees. This is a trigonometric function question, and we know that cotangent is the reciprocal of tangent.

The value of $\cot(90^\circ)$ is undefined.

The value of $\cot(90^\circ)$ is undefined.

#### Steps to Solve

1. Understanding Cotangent Definition

Cotangent is defined as the reciprocal of the tangent function. Therefore, we can write:

$$\cot(\theta) = \frac{1}{\tan(\theta)}$$

1. Find the Value of Tangent at 90 Degrees

We need to calculate the value of $\tan(90^\circ)$. Tangent is the ratio of the sine and cosine functions:

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

At $90^\circ$:

• $\sin(90^\circ) = 1$
• $\cos(90^\circ) = 0$

So,

$$\tan(90^\circ) = \frac{1}{0}$$

which is undefined.

1. Substituting into Cotangent Definition

Given that $\tan(90^\circ)$ is undefined, we can find cotangent:

$$\cot(90^\circ) = \frac{1}{\tan(90^\circ)}$$

Since $\tan(90^\circ)$ is undefined, $\cot(90^\circ)$ is also undefined.

The value of $\cot(90^\circ)$ is undefined.

Cotangent is undefined for angles where tangent is undefined. Since tangent involves division by zero at $90^\circ$, it leads directly to an undefined cotangent.