What is the sin of pi/4 radians? – Trigonometric Functions

What is the sin of pi/4 radians? – Trigonometric Functions

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)/2Share on Facebook

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
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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.

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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.


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