$\cos{(54^\circ)} \,=\, \dfrac{\sqrt{10-2\sqrt{5}}}{4}$

The value of cosine in a fifty four degrees right triangle is called the cosine of angle fifty four degrees.

In Sexagesimal angle measuring system, the angle fifty four degrees is written as $54^\circ$ and the cosine of fifty four degrees is written as $\cos{54^\circ}$. Now, let us learn what the cos $54$ degrees is in trigonometry.

The exact value of cos $54$ degrees is an irrational number and it is written in fraction form as the square root of ten minus two times square root of five divided by four.

$\cos{(54^\circ)} \,=\, \dfrac{\sqrt{10-2\sqrt{5}}}{4}$

The cos $54$ degrees value can be expressed in decimal form as an infinitely extended number but its exact value is approximately considered as follows.

$\cos{(54^\circ)}$ $\,=\,$ $0.5877852522\cdots$

$\implies$ $\cos{(54^\circ)}$ $\,\approx\,$ $0.5878$

In trigonometry, the cos $54$ degrees is also written in two other mathematical forms alternatively.

The cos of $45$ degrees is written as the cosine of three times pi divided by ten radians in circular angle measuring system. So, the sine $3\pi/10$ radians value in surd form is exactly equal to the square root of $10$ minus $2$ times $\sqrt{5}$ divided by $4$ and its value in decimal form is $0.5878$ approximately.

$\cos{\Big(\dfrac{3\pi}{10}\Big)}$ $\,=\,$ $\dfrac{\sqrt{10-2\sqrt{5}}}{4}$ $\,\approx\,$ $0.5878$

In Centesimal system, the cos of fifty four degrees is written as cosine of $60$ grades and the exact value of cos $60$ gradians in fraction is equal to the square root of $10$ minus two times $\sqrt{5}$ divided by $4$, and the cos $60$ grads value in decimal form is equal to $0.5878$ approximately.

$\cos{(60^g)}$ $\,=\,$ $\dfrac{\sqrt{10-2\sqrt{5}}}{4}$ $\,\approx\,$ $0.5878$

Learn how to find the exact value of cosine of angle fifty four degrees as the square root of ten minus two times square root of five divided by four.

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