Cot pi/3

The value of cot pi/3 is 0.5773502. . .. Cot pi/3 radians in degrees is written as cot ((π/3) × 180°/π), i.e., cot (60°). In this article, we will discuss the methods to find the value of cot pi/3 with examples.

• Cot pi/3: 1/√3
• Cot pi/3 in decimal: 0.5773502. . .
• Cot (-pi/3): -0.5773502. . . or -(1/√3)
• Cot pi/3 in degrees: cot (60°)

What is the Value of Cot pi/3?

The value of cot pi/3 in decimal is 0.577350269. . .. Cot pi/3 can also be expressed using the equivalent of the given angle (pi/3) in degrees (60°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/3 radians = pi/3 × (180°/pi) = 60° or 60 degrees
∴ cot pi/3 = cot π/3 = cot(60°) = 1/√3 or 0.5773502. . .

Explanation:

For cot pi/3, the angle pi/3 lies between 0 and pi/2 (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot pi/3 value = 1/√3 or 0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot pi/3 as, cot pi/3 = cot(pi/3 + n × pi), n ∈ Z.
⇒ cot pi/3 = cot 4pi/3 = cot 7pi/3 , and so on.
Note: Since, cotangent is an odd function, the value of cot(-pi/3) = -cot(pi/3).

Methods to Find Value of Cot pi/3

The cotangent function is positive in the 1st quadrant. The value of cot pi/3 is given as 0.57735. . .. We can find the value of cot pi/3 by:

• Using Trigonometric Functions
• Using Unit Circle

Cot pi/3 in Terms of Trigonometric Functions

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

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

Note: Since pi/3 lies in the 1st Quadrant, the final value of cot pi/3 will be positive.

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

• tan (pi/2 - pi/3) = tan pi/6
• -tan (pi/2 + pi/3) = -tan 5pi/6
• -cot (pi - pi/3) = -cot 2pi/3

Cot pi/3 Using Unit Circle

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

• Rotate ‘r’ anticlockwise to form pi/3 angle with the positive x-axis.
• The cot of pi/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 pi/3 = x/y = 0.5774 (approx)

☛ Also Check:

• cos 3pi
• cos 5pi/8
• cos 2pi/8
• tan 5pi/2
• sin 5pi/8
• tan 2pi/3

FAQs on Cot pi/3

What is Cot pi/3?

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

How to Find the Value of Cot pi/3?

The value of cot pi/3 can be calculated by constructing an angle of π/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 pi/3 is equal to the x-coordinate(0.5) divided by the y-coordinate (0.866). ∴ cot pi/3 = 0.5774

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

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

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

☛ Also check: trigonometry table

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

Using trigonometric identities, we can write cot pi/3 in terms of sin pi/3 as, cot(pi/3) = √(1 - sin²(pi/3))/sin pi/3 . Here, the value of sin pi/3 is equal to √3/2.

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

Since the cotangent function can be represented using the cosecant function, we can write cot pi/3 as √(cosec²(pi/3) - 1). The value of cosec pi/3 is equal to 1.15470.