$\sin{(45^\circ)} \,=\, \dfrac{1}{\sqrt{2}}$
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.
A best free mathematics education website for students, teachers and researchers.
Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.
Learn how to solve the maths problems in different methods with understandable steps.
Copyright © 2012 - 2022 Math Doubts, All Rights Reserved