$\sin{(45^\circ)} \,=\, \dfrac{1}{\sqrt{2}}$

The value of sine in a forty five degrees right triangle is called the sine of angle forty five degrees.

The value of sin function when angle of right triangle equals to $45^\circ$ is called sine of angle $45$ degrees. It is written as $\sin{(45^\circ)}$ mathematically in sexagesimal system.

The exact value of sin of $45$ degrees in fraction is $\dfrac{1}{\sqrt{2}}$. It is an irrational number and is equal to $0.7071067812\ldots$ in decimal form. The value of sin of angle $45$ degrees is considered as $0.7071$ approximately in mathematics. The value of $\sin{(45^\circ)}$ is generally called as trigonometric function or trigonometric ratio of standard angle.

$\sin{(45^\circ)}$ is alternatively written as $\sin{\Big(\dfrac{\pi}{4}\Big)}$ in circular system and also written as $\sin{(50^g)}$ in centesimal system.

$(1) \,\,\,$ $\sin{\Big(\dfrac{\pi}{4}\Big)}$ $\,=\,$ $\dfrac{1}{\sqrt{2}}$ $\,=\,$ $0.7071067812\ldots$

$(2) \,\,\,$ $\sin{(50^g)}$ $\,=\,$ $\dfrac{1}{\sqrt{2}}$ $\,=\,$ $0.7071067812\ldots$

You have learnt the exact value of sin of $45$ degrees in both fraction and decimal form. Now, it is time to learn how to derive the value of $\sin{\Big(\dfrac{\pi}{4}\Big)}$ in trigonometry mathematically.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a free math tutor for helping students to learn mathematics online from basics to advanced scientific level for teachers to improve their teaching skill and for researchers to share their research projects.
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.