Cot 4pi/3
The value of cot 4pi/3 is 0.5773502. . .. Cot 4pi/3 radians in degrees is written as cot ((4π/3) × 180°/π), i.e., cot (240°). In this article, we will discuss the methods to find the value of cot 4pi/3 with examples.
- Cot 4pi/3: 1/√3
- Cot 4pi/3 in decimal: 0.5773502. . .
- Cot (-4pi/3): -0.5773502. . . or -(1/√3)
- Cot 4pi/3 in degrees: cot (240°)
What is the Value of Cot 4pi/3?
The value of cot 4pi/3 in decimal is 0.577350269. . .. Cot 4pi/3 can also be expressed using the equivalent of the given angle (4pi/3) in degrees (240°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 4pi/3 radians = 4pi/3 × (180°/pi) = 240° or 240 degrees
∴ cot 4pi/3 = cot 4π/3 = cot(240°) = 1/√3 or 0.5773502. . .
Explanation:
For cot 4pi/3, the angle 4pi/3 lies between pi and 3pi/2 (Third Quadrant). Since cotangent function is positive in the third quadrant, thus cot 4pi/3 value = 1/√3 or 0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot 4pi/3 as, cot 4pi/3 = cot(4pi/3 + n × pi), n ∈ Z.
⇒ cot 4pi/3 = cot 7pi/3 = cot 10pi/3 , and so on.
Note: Since, cotangent is an odd function, the value of cot(-4pi/3) = -cot(4pi/3).
Methods to Find Value of Cot 4pi/3
The cotangent function is positive in the 3rd quadrant. The value of cot 4pi/3 is given as 0.57735. . .. We can find the value of cot 4pi/3 by:
- Using Trigonometric Functions
- Using Unit Circle
Cot 4pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 4pi/3 as:
- cos(4pi/3)/sin(4pi/3)
- ± cos(4pi/3)/√(1 - cos²(4pi/3))
- ± √(1 - sin²(4pi/3))/sin(4pi/3)
- ± 1/√(sec²(4pi/3) - 1)
- ± √(cosec²(4pi/3) - 1)
- 1/tan(4pi/3)
Note: Since 4pi/3 lies in the 3rd Quadrant, the final value of cot 4pi/3 will be positive.
We can use trigonometric identities to represent cot 4pi/3 as,
- tan (pi/2 - 4pi/3) = tan(-5pi/6)
- -tan (pi/2 + 4pi/3) = -tan 11pi/6
- -cot (pi - 4pi/3) = -cot(-pi/3)
Cot 4pi/3 Using Unit Circle
To find the value of cot 4π/3 using the unit circle:
- Rotate ‘r’ anticlockwise to form 4pi/3 angle with the positive x-axis.
- The cot of 4pi/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 4pi/3 = x/y = 0.5774 (approx)
☛ Also Check:
FAQs on Cot 4pi/3
What is Cot 4pi/3?
Cot 4pi/3 is the value of cotangent trigonometric function for an angle equal to 4π/3 radians. The value of cot 4pi/3 is 1/√3 or 0.5774 (approx).
How to Find the Value of Cot 4pi/3?
The value of cot 4pi/3 can be calculated by constructing an angle of 4π/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 4pi/3 is equal to the x-coordinate(-0.5) divided by the y-coordinate (-0.866). ∴ cot 4pi/3 = 0.5774
What is the Value of Cot 4pi/3 in Terms of Cosec 4pi/3?
Since the cotangent function can be represented using the cosecant function, we can write cot 4pi/3 as √(cosec²(4pi/3) - 1). The value of cosec 4pi/3 is equal to -1.15470.
What is the Value of Cot 4pi/3 in Terms of Sin 4pi/3?
Using trigonometric identities, we can write cot 4pi/3 in terms of sin 4pi/3 as, cot(4pi/3) = -√(1 - sin²(4pi/3))/sin 4pi/3 . Here, the value of sin 4pi/3 is equal to -(√3/2).
How to Find Cot 4pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 4pi/3 can be given in terms of other trigonometric functions as:
- cos(4pi/3)/sin(4pi/3)
- ± cos(4pi/3)/√(1 - cos²(4pi/3))
- ± √(1 - sin²(4pi/3))/sin(4pi/3)
- ± 1/√(sec²(4pi/3) - 1)
- ± √(cosec²(4pi/3) - 1)
- 1/tan(4pi/3)
☛ Also check: trigonometric table