Cot pi/6

The value of cot pi/6 is 1.7320508. . .. Cot pi/6 radians in degrees is written as cot ((π/6) × 180°/π), i.e., cot (30°). In this article, we will discuss the methods to find the value of cot pi/6 with examples.

• Cot pi/6: √3
• Cot pi/6 in decimal: 1.7320508. . .
• Cot (-pi/6): -1.7320508. . . or -√3
• Cot pi/6 in degrees: cot (30°)

What is the Value of Cot pi/6?

The value of cot pi/6 in decimal is 1.732050807. . .. Cot pi/6 can also be expressed using the equivalent of the given angle (pi/6) in degrees (30°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/6 radians = pi/6 × (180°/pi) = 30° or 30 degrees
∴ cot pi/6 = cot π/6 = cot(30°) = √3 or 1.7320508. . .

Explanation:

For cot pi/6, the angle pi/6 lies between 0 and pi/2 (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot pi/6 value = √3 or 1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot pi/6 as, cot pi/6 = cot(pi/6 + n × pi), n ∈ Z.
⇒ cot pi/6 = cot 7pi/6 = cot 13pi/6 , and so on.
Note: Since, cotangent is an odd function, the value of cot(-pi/6) = -cot(pi/6).

Methods to Find Value of Cot pi/6

The cotangent function is positive in the 1st quadrant. The value of cot pi/6 is given as 1.73205. . .. We can find the value of cot pi/6 by:

• Using Unit Circle
• Using Trigonometric Functions

Cot pi/6 Using Unit Circle

To find the value of cot π/6 using the unit circle:

• Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.
• The cot of pi/6 equals the x-coordinate(0.866) divided by y-coordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence the value of cot pi/6 = x/y = 1.7321 (approx)

Cot pi/6 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot pi/6 as:

• cos(pi/6)/sin(pi/6)
• ± cos(pi/6)/√(1 - cos²(pi/6))
• ± √(1 - sin²(pi/6))/sin(pi/6)
• ± 1/√(sec²(pi/6) - 1)
• ± √(cosec²(pi/6) - 1)
• 1/tan(pi/6)

Note: Since pi/6 lies in the 1st Quadrant, the final value of cot pi/6 will be positive.

We can use trigonometric identities to represent cot pi/6 as,

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

☛ Also Check:

• tan pi/3
• cos 3pi/8
• sin 3pi/2
• tan pi/2
• tan 11pi 6
• cos 7pi/4

FAQs on Cot pi/6

What is Cot pi/6?

Cot pi/6 is the value of cotangent trigonometric function for an angle equal to π/6 radians. The value of cot pi/6 is √3 or 1.7321 (approx).

How to Find the Value of Cot pi/6?

The value of cot pi/6 can be calculated by constructing an angle of π/6 radians with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cot pi/6 is equal to the x-coordinate(0.866) divided by the y-coordinate (0.5). ∴ cot pi/6 = 1.7321

How to Find Cot pi/6 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot pi/6 can be given in terms of other trigonometric functions as:

• cos(pi/6)/sin(pi/6)
• ± cos(pi/6)/√(1 - cos²(pi/6))
• ± √(1 - sin²(pi/6))/sin(pi/6)
• ± 1/√(sec²(pi/6) - 1)
• ± √(cosec²(pi/6) - 1)
• 1/tan(pi/6)

☛ Also check: trigonometry table

What is the Exact Value of Cot pi/6?

The exact value of cot pi/6 can be given accurately up to 8 decimal places as 1.73205080 or as √3.

What is the Value of Cot pi/6 in Terms of Sin pi/6?

Using trigonometric identities, we can write cot pi/6 in terms of sin pi/6 as, cot(pi/6) = √(1 - sin²(pi/6))/sin pi/6 . Here, the value of sin pi/6 is equal to 1/2.