$\tan{45^\circ}$ value

Exact value

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

Introduction

The value of tangent in a forty five degrees right triangle is called the tan of angle forty five degrees. The angle $45$ degrees is written $45^\circ$ in Sexagesimal system. Therefore, the tan of angle forty five degrees is written as $\tan{45^\circ}$ in trigonometry, and it is time to learn what the tan $45$ degrees value is.

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

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

Other forms

The tan of $45$ degrees is alternatively written in different forms in trigonometry.

Circular system

According to the circular system, the tan of $45$ degrees is written as tan of pi divided by four radians. Hence, the tan of $\pi$ by $4$ radians value is exactly equal to one.

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

Centesimal system

In the same way, the tan of angle $45$ degrees is also written as tan of fifty grades in the centesimal system. So, the exact value of tan of fifty gradians is equal to one.

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

Proof

Learn how to find that the tan of angle forty five degrees is exactly equal to one by constructing a right angled triangle with an angle of $45$ degrees.

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Jun 26, 2023

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