$\cos{(18^°)}$ $\,=\,$ $\dfrac{\sqrt{10+2\sqrt{5}}}{4}$

The value of cosine in an eighteen degrees right triangle is called the cosine of angle eighteen degrees.

The cosine of angle eighteen degrees is a value that represents the ratio of length of adjacent side to length of hypotenuse when the angle of a right triangle (or right angled triangle) is eighteen degrees.

The cosine of angle eighteen degrees is written as $\cos{(18^°)}$ in trigonometry as per the sexagesimal system and its exact value in fraction form is quotient of square root of ten plus two times square root of five by four. Hence, it is written mathematically in the following form.

$\cos{(18^°)}$ $\,=\,$ $\dfrac{\sqrt{10+2\sqrt{5}}}{4}$

The cos of eighteen degrees value is exactly an irrational number and its value can be written in decimal form too as follows.

$\implies$ $\cos{(18^°)}$ $\,=\,$ $0.9510565162\ldots$

$\implies$ $\cos{(18^°)}$ $\,\approx\,$ $0.9511$

The cosine eighteen degrees is also written in two other forms in trigonometric mathematics.

The cos of eighteen degrees can be written as the cos of quotient of pi by ten radian as per the circular system. So, it is written in mathematical form as $\sin{\Big(\dfrac{\pi}{10}\Big)}$.

$\cos{\Big(\dfrac{\pi}{10}\Big)}$ $\,=\,$ $\dfrac{\sqrt{10+2\sqrt{5}}}{4}$

On the basis of the centesimal system, the cosine of angle eighteen degrees is written as cos of angle twenty grades. Therefore, it is written as $\cos{\Big(20^g\Big)}$ in mathematical form.

$\cos{\Big(20^g\Big)}$ $\,=\,$ $\dfrac{\sqrt{10+2\sqrt{5}}}{4}$

The exact value of cosine of eighteen degrees can be derived in two distinct methods in mathematics.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.