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.

Answer

The value of $\cot(90^\circ)$ is undefined.
Answer for screen readers

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.

More Information

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.

Tips

  • Confusing the definitions of cotangent and tangent can lead to incorrect conclusions. Always remember that cotangent is the reciprocal of tangent.
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