Cot 2pi/3

The value of cot 2pi/3 is -0.5773502. . .. Cot 2pi/3 radians in degrees is written as cot ((2π/3) × 180°/π), i.e., cot (120°). In this article, we will discuss the methods to find the value of cot 2pi/3 with examples.

• Cot 2pi/3: -(1/√3)
• Cot 2pi/3 in decimal: -0.5773502. . .
• Cot (-2pi/3): 0.5773502. . . or 1/√3
• Cot 2pi/3 in degrees: cot (120°)

What is the Value of Cot 2pi/3?

The value of cot 2pi/3 in decimal is -0.577350269. . .. Cot 2pi/3 can also be expressed using the equivalent of the given angle (2pi/3) in degrees (120°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 2pi/3 radians = 2pi/3 × (180°/pi) = 120° or 120 degrees
∴ cot 2pi/3 = cot 2π/3 = cot(120°) = -(1/√3) or -0.5773502. . .

Explanation:

For cot 2pi/3, the angle 2pi/3 lies between pi/2 and pi (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 2pi/3 value = -(1/√3) or -0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot 2pi/3 as, cot 2pi/3 = cot(2pi/3 + n × pi), n ∈ Z.
⇒ cot 2pi/3 = cot 5pi/3 = cot 8pi/3 , and so on.
Note: Since, cotangent is an odd function, the value of cot(-2pi/3) = -cot(2pi/3).

Methods to Find Value of Cot 2pi/3

The cotangent function is negative in the 2nd quadrant. The value of cot 2pi/3 is given as -0.57735. . .. We can find the value of cot 2pi/3 by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 2pi/3 Using Unit Circle

To find the value of cot 2π/3 using the unit circle:

• Rotate ‘r’ anticlockwise to form 2pi/3 angle with the positive x-axis.
• The cot of 2pi/3 equals the x-coordinate(-0.5) divided by y-coordinate(0.866) of the point of intersection (-0.5, 0.866) of unit circle and r.

Hence the value of cot 2pi/3 = x/y = -0.5774 (approx)

Cot 2pi/3 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 2pi/3 as:

• cos(2pi/3)/sin(2pi/3)
• ± cos(2pi/3)/√(1 - cos²(2pi/3))
• ± √(1 - sin²(2pi/3))/sin(2pi/3)
• ± 1/√(sec²(2pi/3) - 1)
• ± √(cosec²(2pi/3) - 1)
• 1/tan(2pi/3)

Note: Since 2pi/3 lies in the 2nd Quadrant, the final value of cot 2pi/3 will be negative.

We can use trigonometric identities to represent cot 2pi/3 as,

• tan (pi/2 - 2pi/3) = tan(-pi/6)
• -tan (pi/2 + 2pi/3) = -tan 7pi/6
• -cot (pi - 2pi/3) = -cot pi/3

☛ Also Check:

• sec pi/4
• cos 7pi/12
• sin 7pi/2
• sin 2pi
• sin 17pi/12
• cos 9pi/2

FAQs on Cot 2pi/3

What is Cot 2pi/3?

Cot 2pi/3 is the value of cotangent trigonometric function for an angle equal to 2π/3 radians. The value of cot 2pi/3 is -(1/√3) or -0.5774 (approx).

How to Find Cot 2pi/3 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 2pi/3 can be given in terms of other trigonometric functions as:

• cos(2pi/3)/sin(2pi/3)
• ± cos(2pi/3)/√(1 - cos²(2pi/3))
• ± √(1 - sin²(2pi/3))/sin(2pi/3)
• ± 1/√(sec²(2pi/3) - 1)
• ± √(cosec²(2pi/3) - 1)
• 1/tan(2pi/3)

☛ Also check: trigonometric table

How to Find the Value of Cot 2pi/3?

The value of cot 2pi/3 can be calculated by constructing an angle of 2π/3 radians with the x-axis, and then finding the coordinates of the corresponding point (-0.5, 0.866) on the unit circle. The value of cot 2pi/3 is equal to the x-coordinate(-0.5) divided by the y-coordinate (0.866). ∴ cot 2pi/3 = -0.5774

What is the Value of Cot 2pi/3 in Terms of Tan 2pi/3?

Since the cotangent function is the reciprocal of the tangent function, we can write cot 2pi/3 as 1/tan(2pi/3). The value of tan 2pi/3 is equal to -√3.

What is the Value of Cot 2pi/3 in Terms of Sec 2pi/3?

We can represent the cotangent function in terms of the secant function using trig identities, cot 2pi/3 can be written as -1/√(sec²(2pi/3) - 1). Here, the value of sec 2pi/3 is equal to -2.