Math Doubts

$\csc{(90^°)}$ value

The cosecant value when angle of a right triangle equals to $90^°$ is called cosecant of angle $90$ degrees. It is written as $\csc{(90^°)}$ or $\cosec{(90^°)}$ as per sexagesimal system.

$\csc{(90^°)} \,=\, 1$

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 $\sin{(45^°)}$ is generally called as trigonometric function or trigonometric ratio of standard angle.

Alternative form

$\sin{(45^°)}$ 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.

Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved