For the sine of 45 degrees we use the abbreviation *sin* for the trigonometric function together with the degree symbol °, and write it as sin 45°.

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If you have been looking for *what is sin 45°*, or if you have been wondering about sin 45 degrees in radians, then you are right here, too.

In this post you can find the sin 45° value, along with identities.

Read on to learn all about the sin of 45°.

## Sin 45 Degrees

If you want to know *what is sin 45 degrees* in terms of trigonometry, then navigate straight to the explanations in the next paragraph; what’s ahead in this section is the value of sin 45°:

sin45° = √(2)/2sin 45° = √(2)/2sin 45 degrees = √(2)/2″ onclick=”if (!window.__cfRLUnblockHandlers) return false; return fbs_click()” target=”_blank” rel=”nofollow noopener noreferrer” data-cf-modified-4375686b3058581a271a1ca7-=””>

The sin of 45 degrees is √(2)/2, the same as sin of 45 degrees in radians. To obtain 45 degrees in radian multiply 45° by $pi$ / 180° = 1/4 $pi$. Sin 45degrees = sin (1/4 × $pi)$.

Our results of sin45° have been rounded to five decimal places. If you want sine 45° with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate sin 45 degrees insert the angle 45 in the field labelled °, but if you want to calculate sin 45 in radians, then you have to press the swap unit button first.

### Calculate sin

° :

A Really Cool Sine Calculator and Useful Information! Please ReTweet. Click To TweetBesides sin45°, similar trigonometric calculations on our site include, but are not limited, to:

The identities of sine 45° are as follows:sin45°= cos (90°-45°) = cos 45°= sin (180°-45°) = sin 135°

-sin45°= cos (90°+45°) = cos 135°= sin (180°+45°) = sin 225°Note that sin45° is periodic: sin (45° + *n* × 360°) = sin 45 degrees, n$hspace{5px} in hspace{5px} mathbb{Z}$.

There are more formulas for the double angle (2 × 45°), half angle ((45/2)°) as well as the sum, difference and products of two angles such as 45° and β.

You can locate all of them in the respective article found in the header menu. To find everything about sin -45° click the link. And here is all about cos 45°, including, for instance, a converter.

In terms of the other five trigonometric functions, sin of 45° =

$pm sqrt{1-cos^{2} 45 ^circ}$ $pmfrac{ an 45^circ}{sqrt{1 + an^{2} 45^circ}}$ $pmfrac{1}{sqrt{1 + cot^{2} 45^circ}}$ $pmfrac{sqrt{sec^{2} 45^circ – 1} }{sec 45^circ}$ $frac{1}{csc 45^circ}$

As the cosecant function is the reciprocal of the sine function, 1 / csc 45° = sin45°.

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In the next part of this article of this article we discuss the trigonometric significance of sin45°, and there you can also learn what the search calculations form in the sidebar is used for.

## What is sin 45°?

In a triangle which has one angle of 90 degrees, the sine of the angle of 45° is the ratio of the length of the opposite side *o* to the length of the hypotenuse *h*: sin 45° = o/h.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 45 degrees is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.

As detailed in the unit-circle definition on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, y = sin 45°.

Bringing together the triangle definition and the unit circle definition of sine 45 degrees, o = y and h = r = 1. It follows that $yhspace{5px} =hspace{5px}frac{opposite}{hypotenuse}hspace{5px}=hspace{5px}sin 45^circ$.

Note that you can locate many terms including the sine45° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of sin45°.

Along the same lines, using the aforementioned form, can you look up terms such as sin 45° value, sin 45, sin45° value and *what is the sin of 45 degrees*, just to name a few.

Given the periodic property of sine of 45°, to determine the sine of an angle > 360°, e.g. 765°, calculate sin 765° as sin (765 Mod 360)° = sine of 45°, or look it up with our form.

## Conclusion

The frequently asked questions in the context include *what is sin 45 degrees* and *what is the sin of 45 degrees* for example; reading our content they are no-brainers.

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