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 Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved