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
- Understanding Cotangent Definition
Cotangent is defined as the reciprocal of the tangent function. Therefore, we can write:
$$ \cot(\theta) = \frac{1}{\tan(\theta)} $$
- 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.
- 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.