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Welcome to sin 3pi/4, our post aboutthe sine of 3pi/4 radians.
For the sine of 3pi/4 radians we use the abbreviation sin for the trigonometric function and write it as sin 3pi/4.
If you have been looking for what is sin 3pi/4, or if you have been wondering about sin 3pi/4 radians in degrees, then you are right here, too.
In this post you can find the sin 3pi/4 value, along with identities.
Read on to learn all about the sin of 3pi/4.
Sin 3Pi/4 Radians
If you want to know what is sin 3pi/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 3pi/4:
sin 3pi/4 = √(2)/2
sin 3pi/4 radians = √(2)/2
The sin of 3pi/4 radians is √(2)/2, the same as sin of 3pi/4 radians in degrees. To change 3pi/4 radians to degrees multiply 3pi/4 by 180° / $\pi$ = 135°. Sin 3pi/4 = sin 135 degrees.
Our results of sin3pi/4 have been rounded to five decimal places. If you want sine 3pi/4 with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate sin 3pi/4 radians insert the angle 3pi/4 in decimal notation, but if you want to calculate sin 3pi/4 in degrees, then you have to press the swap unit button first.
Calculate sin [radians]
The identities of sine 3pi/4 are as follows:
= cos (pi/2 – 3pi/4) = cos -1/4 pi
= sin (pi – 3pi/4) = sin 1/4 pi
-sin3pi/4
= cos (pi/2 + 3pi/4) = cos 5/4 pi
= sin (pi + 3pi/4) = sin 7/4 pi
There are more formulas for the double angle (2 × 3pi/4), half angle ((3pi/4/2)) as well as the sum, difference and products of two angles such as 3pi/4 and β.
You can locate all of them in the respective article found in the header menu. To find everything about sin -3pi/4 click the link. And here is all about cos 3pi/4, including, for instance, a converter.
In terms of the other five trigonometric functions, sin of 3pi/4 =
- $\pm \sqrt{1-\cos^{2} 3\pi/4}$
- $\pm\frac{\tan 3\pi/4}{\sqrt{1 + \tan^{2} 3\pi/4}}$
- $\pm\frac{1}{\sqrt{1 + \cot^{2} 3\pi/4}}$
- $\pm\frac{\sqrt{\sec^{2} (3\pi/4) – 1} }{\sec 3\pi/4}$
- $\frac{1}{\csc 3\pi/4}$
As the cosecant function is the reciprocal of the sine function, 1 / csc 3pi/4 = sin3pi/4.
In the next part of this article of this article we discuss the trigonometric significance of sin3pi/4, and there you can also learn what the search calculations form in the sidebar is used for.
What is sin 3Pi/4?
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 3pi/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 3pi/4.
Note that you can locate many terms including the sine3pi/4 value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of sin3pi/4.
Along the same lines, using the aforementioned form, can you look up terms such as sin 3pi/4 value, sin 3pi/4, sin3pi/4 value and what is the sin of 3pi/4 radians, just to name a few.
Given the periodic property of sine of 3pi/4, to determine the sine of an angle > 2pi, e.g. 19/4 pi, calculate sin 19/4 pi as sin (19/4 pi mod 2pi) = sine of 3pi/4, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is sin 3pi/4 radians and what is the sin of 3pi/4 radians for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 26th, 2017