Math Doubts

$\sin{54^\circ}$ value

Exact value

$\sin{(54^\circ)} \,=\, \dfrac{\sqrt{5}+1}{4}$


The value of sine in a $54$ degrees right triangle is called the sine of angle fifty four degrees. The fifty four degrees is written as $54^\circ$ as per Sexagesimal system and the sine of fifty four degrees is written as $\sin{54^\circ}$ mathematically in trigonometry. It is time to learn what the sin $54$ degrees value is.

Fraction form

The trigonometric function sine $54$ degrees value is a fraction in irrational form and its exact value is equal to the square root of $5$ plus $1$ divided by $4$.

$\sin{54^\circ}$ $\,=\,$ $\dfrac{\sqrt{5}+1}{4}$

Decimal form

The exact value of sin $54$ degrees is expressed as a fraction in radical form and it can be expressed in decimal form as follows.

$\sin{(54^\circ)}$ $\,=\,$ $0.8090169943\ldots$

$\implies$ $\sin{(54^\circ)}$ $\,\approx\,$ $0.809$

sin 54 degrees value

Other forms

Let’s learn how to write sine of angle fifty four degrees alternatively in two other forms.

Circular system

According to the circular system, the sine of $54$ degrees is written as sine of three times pi divided by ten radians, and the exact value of the sin $3\pi$ divided by $10$ in surd form is $\sqrt{5}$ plus $1$ divided by $10$. Similarly, its exact value in decimal form is approximately equal to $0.809$.

$\sin{\bigg(\dfrac{3\pi}{10}\bigg)}$ $\,=\,$ $\dfrac{\sqrt{5}+1}{4}$ $\,\approx\,$ $0.809$

Centesimal system

Likewise, the sine of angle $54$ degrees is also written as the sine of sixty gradians in the centesimal system. So, the exact value of sine $60$ grades in irrational fraction form is equal to the square root of five plus one divided by ten and the approximate value of sine $60$ grads in decimal form is $0.809$.

$\sin{(60^g)}$ $\,=\,$ $\,=\,$ $\dfrac{\sqrt{5}+1}{4}$ $\,\approx\,$ $0.809$


Let’s learn how to find the exact value of sin $54$ degrees in both trigonometric and geometric methods.

Math Doubts

A best free mathematics education website that helps students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved