Cot 60 Degrees

The value of cot 60 degrees is 0.5773502. . .. Cot 60 degrees in radians is written as cot (60° × π/180°), i.e., cot (π/3) or cot (1.047197. . .). In this article, we will discuss the methods to find the value of cot 60 degrees with examples.

• Cot 60°: 1/√3
• Cot 60° in decimal: 0.5773502. . .
• Cot (-60 degrees): -0.5773502. . . or -(1/√3)
• Cot 60° in radians: cot (π/3) or cot (1.0471975 . . .)

What is the Value of Cot 60 Degrees?

The value of cot 60 degrees in decimal is 0.577350269. . .. Cot 60 degrees can also be expressed using the equivalent of the given angle (60 degrees) in radians (1.04719 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 60 degrees = 60° × (π/180°) rad = π/3 or 1.0471 . . .
∴ cot 60° = cot(1.0471) = 1/√3 or 0.5773502. . .

Explanation:

For cot 60 degrees, the angle 60° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 60° value = 1/√3 or 0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot 60° as, cot 60 degrees = cot(60° + n × 180°), n ∈ Z.
⇒ cot 60° = cot 240° = cot 420°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-60°) = -cot(60°).

Methods to Find Value of Cot 60 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 60° is given as 0.57735. . . We can find the value of cot 60 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cot 60° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 60 degrees as:

• cos(60°)/sin(60°)
• ± cos 60°/√(1 - cos²(60°))
• ± √(1 - sin²(60°))/sin 60°
• ± 1/√(sec²(60°) - 1)
• ± √(cosec²(60°) - 1)
• 1/tan 60°

Note: Since 60° lies in the 1st Quadrant, the final value of cot 60° will be positive.

We can use trigonometric identities to represent cot 60° as,

• tan (90° - 60°) = tan 30°
• -tan (90° + 60°) = -tan 150°
• -cot (180° - 60°) = -cot 120°

Cot 60 Degrees Using Unit Circle

To find the value of cot 60 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 60° angle with the positive x-axis.
• The cot of 60 degrees 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 60° = x/y = 0.5774 (approx).

☛ Also Check:

• cot 360 degrees
• cot 75 degrees
• cot 45 degrees
• cot 3 degrees
• cot 15 degrees
• cot 225 degrees

FAQs on Cot 60 Degrees

What is Cot 60 Degrees?

Cot 60 degrees is the value of cotangent trigonometric function for an angle equal to 60 degrees. The value of cot 60° is 1/√3 or 0.5774 (approx).

How to Find Cot 60° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 60° can be given in terms of other trigonometric functions as:

• cos(60°)/sin(60°)
• ± cos 60°/√(1 - cos²(60°))
• ± √(1 - sin²(60°))/sin 60°
• ± 1/√(sec²(60°) - 1)
• ± √(cosec²(60°) - 1)
• 1/tan 60°

☛ Also check: trigonometric table

What is the Value of Cot 60° in Terms of Cosec 60°?

Since the cotangent function can be represented using the cosecant function, we can write cot 60° as √(cosec²(60°) - 1). The value of cosec 60° is equal to 1.15470.

How to Find the Value of Cot 60 Degrees?

The value of cot 60 degrees can be calculated by constructing an angle of 60° 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 60° is equal to the x-coordinate(0.5) divided by the y-coordinate (0.866). ∴ cot 60° = 0.5774

What is the Value of Cot 60 Degrees in Terms of Tan 60°?

Since the cotangent function is the reciprocal of the tangent function, we can write cot 60° as 1/tan(60°). The value of tan 60° is equal to √3.