Welcome to **sin pi/4**, our post aboutthe sine of pi/4 radians.

For the sine of pi/4 radians we use the abbreviation sin for the trigonometric function and write it as sin pi/4.

If you have been looking for what is sin pi/4, or if you have been wondering about sin pi/4 radians in degrees, then you are right here, too.

In this post you can find the sin pi/4 value, along with identities.

Read on to learn all about the sin of pi/4.

## Sin Pi/4 Radians

If you want to know what is sin pi/4 radians 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 pi/4:

sinpi/4 = √(2)/2sin pi/4 = √(2)/2sin pi/4 radians = √(2)/2

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

Our results of sinpi/4 have been rounded to five decimal places. If you want sine pi/4 with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate sin pi/4 radians insert the angle pi/4 in decimal notation, but if you want to calculate sin pi/4 in degrees, then you have to press the swap unit button first.

A Really Cool Sine Calculator and Useful Information! Please ReTweet. Click To TweetBesides sinpi/4, similar trigonometric calculations on our site include, but are not limited, to:

- Sin -3.97
- Sin -514°
- Sin 1.54

The identities of sine pi/4 are as follows:

sinpi/4= cos (pi/2 – pi/4) = cos 1/4 pi= sin (pi – pi/4) = sin 3/4 pi

-sinpi/4= cos (pi/2 + pi/4) = cos 3/4 pi= sin (pi + pi/4) = sin 5/4 pi

Note that sinpi/4 is periodic: sin (pi/4 + n × 2pi) = sin pi/4, n$hspace{5px} in hspace{5px} mathbb{Z}$.

There are more formulas for the double angle (2 × pi/4), half angle ((pi/4/2)) as well as the sum, difference and products of two angles such as pi/4 and β.

You can locate all of them in the respective article found in the header menu. To find everything about sin -pi/4 click the link. And here is all about cos pi/4, including, for instance, a converter.

In terms of the other five trigonometric functions, sin of pi/4 =

- $pm sqrt{1-cos^{2} pi/4}$
- $pmfrac{tan pi/4}{sqrt{1 + tan^{2} pi/4}}$
- $pmfrac{1}{sqrt{1 + cot^{2} pi/4}}$
- $pmfrac{sqrt{sec^{2} (pi/4) – 1} }{sec pi/4}$
- $frac{1}{csc pi/4}$

As the cosecant function is the reciprocal of the sine function, 1 / csc pi/4 = sinpi/4.

In the next part of this article of this article we discuss the trigonometric significance of sinpi/4, and there you can also learn what the search calculations form in the sidebar is used for.

## What is sin Pi/4?

In a triangle which has one angle of pi/2, the sine of the angle of pi/4 is the ratio of the length of the opposite side o to the length of the hypotenuse h: sin pi/4 = o/h.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, pi/4 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 pi/4.

Bringing together the triangle definition and the unit circle definition of sine pi/4, o = y and h = r = 1. It follows that $yhspace{5px} =hspace{5px}frac{opposite}{hypotenuse}hspace{5px}=hspace{5px}sin pi/4$.

Note that you can locate many terms including the sinepi/4 value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of sinpi/4.

Along the same lines, using the aforementioned form, can you look up terms such as sin pi/4 value, sin pi/4, sinpi/4 value and what is the sin of pi/4 radians, just to name a few.

Given the periodic property of sine of pi/4, to determine the sine of an angle > 2pi, e.g. 17/4 pi, calculate sin 17/4 pi as sin (17/4 pi mod 2pi) = sine of pi/4, or look it up with our form.

## Conclusion

The frequently asked questions in the context include what is sin pi/4 radians and what is the sin of pi/4 radians for example; reading our content they are no-brainers.

But, if there is something else about sine pi/4 you would like to know, fill in the form on the bottom of this post, or send us an email with a subject line such as sine pi/4 radians.

If our calculator and the information on sinpi/4 have been helpful, please hit the sharing buttons to spread the word about our content, and don’t forget to bookmark us.

Or, even better, install absolutely free PWA app (see menu or sidebar)!

Leave this field empty if you’re human: Thanks for visiting sinpi/4 radians.