Math Doubts

$\sin{45^\circ}$ value

Exact value

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


The value of sine in a $45$ degrees right triangle (or right angled triangle) is called the sine of angle forty five degrees. In sexagesimal system, the angle forty five degrees is written as $45^\circ$. So, the sine of angle forty five degrees is written as $\sin{45^\circ}$ in trigonometry. Now, let’s learn what the sin $45$ degrees value is.

Fraction form

The exact value of sin $45$ degrees in fraction form is written as a fraction in radical form, and it is equal to $1$ divided by square root of $2$.

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

Decimal form

The trigonometric function sine for a standard angle $45$ degrees value is an irrational number. So, it can also be evaluated in decimal form as follows.

$\sin{(45^\circ)}$ $\,=\,$ $0.7071067812\ldots$

$\implies$ $\sin{(45^\circ)}$ $\,\approx\,$ $0.7071$

sin 45 degrees value

Other forms

The sine of $45$ degrees can be written in trigonometry alternatively in two different forms.

Circular system

The sine of angle $45$ degrees is written as sine of pi divided by four radians in circular system. So, the sine of $\pi$ divided by $4$ radians is equal to $1$ divided by square root of $2$ in fraction form and its value in decimal form is equal to $0.7071$ approximately.

$\sin{\Big(\dfrac{\pi}{4}\Big)}$ $\,=\,$ $\dfrac{1}{\sqrt{2}}$ $\,\approx\,$ $0.7071$

Centesimal system

Similarly, the sine of $45$ degrees is also written as sine of $50$ gradians as per centesimal system. Therefore, the exact value of sine of fifty grades is equal to one divided by square root of two in fraction form and sine of $50$ grads is approximately equal to $0.7071$ in decimal form.

$\sin{(50^g)}$ $\,=\,$ $\dfrac{1}{\sqrt{2}}$ $\,\approx\,$ $0.7071$


Learn how to find the exact value of sine $45$ degrees as an irrational fraction one divided by square root of two by constructing a right triangle with an angle forty five degrees.

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved