$\cot{45^\circ}$ value

Exact value

$\cot{45^\circ} \,=\, 1$

Introduction

The value of cotangent in a forty five degrees right angled triangle is called the cot of angle forty five degrees. In sexagesimal system, the angle $45$ degrees is written as $45^\circ$. So, the cot of angle forty five degrees is expressed as $\cot{45^\circ}$ in trigonometry. Now, let’s learn what the cot $45$ degrees value is.

$\cot{(45^\circ)} \,=\, 1$

The exact value of cot $45$ degrees is an integer, and it is equal to $1$. So, no need to write the cot $45$ degrees value in either decimal or fraction form.

Other forms

In trigonometry, the cot of $45$ degrees value is written alternatively in two distinct forms.

Circular system

The cotangent of forty degrees is written as cot of pi divided by four radians in circular system. So, the exact value of cot of $\pi$ divided by $4$ radians is equal to one.

$\cot{\Big(\dfrac{\pi}{4}\Big)} \,=\, 1$

Centesimal system

Likewise, the cot of angle $45$ degrees is also expressed as cot of fifty gradians as per centesimal angle measuring system. Therefore, the exact value of cot $50$ grades is equal to one.

$\cot{(50^g)} \,=\, 1$

Proof

Learn how to find that the exact value of cot forty five degrees is equal to one by constructing a right triangle with an angle of $45^\circ$.

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