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Welcome to sin 4pi/3, our post aboutthe sine of 4pi/3 radians.
For the sine of 4pi/3 radians we use the abbreviation sin for the trigonometric function and write it as sin 4pi/3.
If you have been looking for what is sin 4pi/3, or if you have been wondering about sin 4pi/3 radians in degrees, then you are right here, too.
In this post you can find the sin 4pi/3 value, along with identities.
Read on to learn all about the sin of 4pi/3.
Sin 4Pi/3 Radians
If you want to know what is sin 4pi/3 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 4pi/3:
sin 4pi/3 = -√(3)/2
sin 4pi/3 radians = -√(3)/2
The sin of 4pi/3 radians is -√(3)/2, the same as sin of 4pi/3 radians in degrees. To change 4pi/3 radians to degrees multiply 4pi/3 by 180° / $\pi$ = 240°. Sin 4pi/3 = sin 240 degrees.
Our results of sin4pi/3 have been rounded to five decimal places. If you want sine 4pi/3 with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate sin 4pi/3 radians insert the angle 4pi/3 in decimal notation, but if you want to calculate sin 4pi/3 in degrees, then you have to press the swap unit button first.
Calculate sin [radians]
The identities of sine 4pi/3 are as follows:
= cos (pi/2 – 4pi/3) = cos -5/6 pi
= sin (pi – 4pi/3) = sin -1/3 pi
-sin4pi/3
= cos (pi/2 + 4pi/3) = cos 11/6 pi
= sin (pi + 4pi/3) = sin 7/3 pi
There are more formulas for the double angle (2 × 4pi/3), half angle ((4pi/3/2)) as well as the sum, difference and products of two angles such as 4pi/3 and β.
You can locate all of them in the respective article found in the header menu. To find everything about sin -4pi/3 click the link. And here is all about cos 4pi/3, including, for instance, a converter.
In terms of the other five trigonometric functions, sin of 4pi/3 =
- $\pm \sqrt{1-\cos^{2} 4\pi/3}$
- $\pm\frac{\tan 4\pi/3}{\sqrt{1 + \tan^{2} 4\pi/3}}$
- $\pm\frac{1}{\sqrt{1 + \cot^{2} 4\pi/3}}$
- $\pm\frac{\sqrt{\sec^{2} (4\pi/3) – 1} }{\sec 4\pi/3}$
- $\frac{1}{\csc 4\pi/3}$
As the cosecant function is the reciprocal of the sine function, 1 / csc 4pi/3 = sin4pi/3.
In the next part of this article of this article we discuss the trigonometric significance of sin4pi/3, and there you can also learn what the search calculations form in the sidebar is used for.
What is sin 4Pi/3?
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 4pi/3 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 4pi/3.
Note that you can locate many terms including the sine4pi/3 value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of sin4pi/3.
Along the same lines, using the aforementioned form, can you look up terms such as sin 4pi/3 value, sin 4pi/3, sin4pi/3 value and what is the sin of 4pi/3 radians, just to name a few.
Given the periodic property of sine of 4pi/3, to determine the sine of an angle > 2pi, e.g. 16/3 pi, calculate sin 16/3 pi as sin (16/3 pi mod 2pi) = sine of 4pi/3, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is sin 4pi/3 radians and what is the sin of 4pi/3 radians for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 26th, 2017