The value of sine function when angle of right triangle equals to $18^°$ is called sin of angle $18$ degrees. In mathematics, it is written as $\sin{(18^°)}$ as per sexagesimal system.

$\sin{(18^°)} \,=\, \dfrac{\sqrt{5}-1}{4}$

It is an exact value of sin of $18$ degrees in fraction. Actually, it is an irrational number and equals to $0.3090169943\ldots$ in decimal form. In mathematics, the approximate value of sin of angle $18$ degrees is considered as $0.30902$.

The $\sin{(18^°)}$ is expressed alternatively as $\sin{\Big(\dfrac{\pi}{18}\Big)}$ in circular system and also expressed as $\sin{(20^g)}$ in centesimal system.

$(1) \,\,\,$ $\sin{\Big(\dfrac{\pi}{18}\Big)}$ $\,=\,$ $\dfrac{\sqrt{5}-1}{4}$ $\,=\,$ $0.3090169943\ldots$

$(2) \,\,\,$ $\sin{(20^g)}$ $\,=\,$ $\dfrac{\sqrt{5}-1}{4}$ $\,=\,$ $0.3090169943\ldots$

Now, you know the exact value of $\sin{\Big(\dfrac{\pi}{18}\Big)}$ and it is time to learn how to derive the exact value of sin $18$ degrees in trigonometry.

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.