The value of sin 2pi/3 is 0.8660254. . .

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. Sin 2pi/3 radians in levels is composed as sin ((2π/3) × 180°/π), i.e., sin (120°). In this article, we will comment on the techniques to uncover the value of sin 2pi/3 v examples.

Sin 2pi/3: √3/2Sin 2pi/3 in decimal: 0.8660254. . .Sin (-2pi/3): -0.8660254. . . Or -(√3/2)Sin 2pi/3 in degrees: sin (120°)

What is the value of Sin 2pi/3?

The worth of sin 2pi/3 in decimal is 0.866025403. . .. Sin 2pi/3 can additionally be expressed utilizing the equivalent of the offered angle (2pi/3) in levels (120°).

We know, using radian to level conversion, θ in degrees = θ in radians × (180°/pi)⇒ 2pi/3 radians = 2pi/3 × (180°/pi) = 120° or 120 degrees∴ sin 2pi/3 = sin 2π/3 = sin(120°) = √3/2 or 0.8660254. . .

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Explanation:

For sin 2pi/3, the edge 2pi/3 lies between pi/2 and pi (Second Quadrant). Because sine role is hopeful in the second quadrant, hence sin 2pi/3 value = √3/2 or 0.8660254. . .Since the sine role is a periodic function, we can represent sin 2pi/3 as, sin 2pi/3 = sin(2pi/3 + n × 2pi), n ∈ Z.⇒ sin 2pi/3 = sin 8pi/3 = sin 14pi/3 , and also so on.Note: Since, sine is an odd function, the value of sin(-2pi/3) = -sin(2pi/3).

Methods to find Value that Sin 2pi/3

The sine function is positive in the second quadrant. The worth of sin 2pi/3 is provided as 0.86602. . .. Us can discover the value of sin 2pi/3 by:

Using Unit CircleUsing Trigonometric Functions

Sin 2pi/3 making use of Unit Circle

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To uncover the worth of sin 2π/3 making use of the unit circle:

Rotate ‘r’ anticlockwise to form 2pi/3 angle through the hopeful x-axis.The sin the 2pi/3 equals the y-coordinate(0.866) of the suggest of intersection (-0.5, 0.866) that unit circle and also r.

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Hence the worth of sin 2pi/3 = y = 0.866 (approx)

Sin 2pi/3 in regards to Trigonometric Functions

Using trigonometry formulas, we have the right to represent the sin 2pi/3 as:

± √(1-cos²(2pi/3))± tan(2pi/3)/√(1 + tan²(2pi/3))± 1/√(1 + cot²(2pi/3))± √(sec²(2pi/3) - 1)/sec(2pi/3)1/cosec(2pi/3)

Note: since 2pi/3 lies in the second Quadrant, the final value of sin 2pi/3 will be positive.

We deserve to use trigonometric identities to represent sin 2pi/3 as,

sin(pi - 2pi/3) = sin pi/3-sin(pi + 2pi/3) = -sin 5pi/3cos(pi/2 - 2pi/3) = cos(-pi/6)-cos(pi/2 + 2pi/3) = -cos 7pi/6

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