Cot 6 Degrees

The value of cot 6 degrees is 9.5143644. . .. Cot 6 degrees in radians is written as cot (6° × π/180°), i.e., cot (π/30) or cot (0.104719. . .). In this article, we will discuss the methods to find the value of cot 6 degrees with examples.

• Cot 6° in decimal: 9.5143644. . .
• Cot (-6 degrees): -9.5143644. . .
• Cot 6° in radians: cot (π/30) or cot (0.1047197 . . .)

What is the Value of Cot 6 Degrees?

The value of cot 6 degrees in decimal is 9.514364454. . .. Cot 6 degrees can also be expressed using the equivalent of the given angle (6 degrees) in radians (0.10471 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 6 degrees = 6° × (π/180°) rad = π/30 or 0.1047 . . .
∴ cot 6° = cot(0.1047) = 9.5143644. . .

Explanation:

For cot 6 degrees, the angle 6° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 6° value = 9.5143644. . .
Since the cotangent function is a periodic function, we can represent cot 6° as, cot 6 degrees = cot(6° + n × 180°), n ∈ Z.
⇒ cot 6° = cot 186° = cot 366°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-6°) = -cot(6°).

Methods to Find Value of Cot 6 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 6° is given as 9.51436. . . We can find the value of cot 6 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cot 6° in Terms of Trigonometric Functions

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

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

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

We can use trigonometric identities to represent cot 6° as,

• tan (90° - 6°) = tan 84°
• -tan (90° + 6°) = -tan 96°
• -cot (180° - 6°) = -cot 174°

Cot 6 Degrees Using Unit Circle

To find the value of cot 6 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 6° angle with the positive x-axis.
• The cot of 6 degrees equals the x-coordinate(0.9945) divided by y-coordinate(0.1045) of the point of intersection (0.9945, 0.1045) of unit circle and r.

Hence the value of cot 6° = x/y = 9.5144 (approx).

☛ Also Check:

• cot 30 degrees
• cot 0 degrees
• cot 15 degrees
• cot 50 degrees
• cot 10 degrees
• cot 238 degrees

FAQs on Cot 6 Degrees

What is Cot 6 Degrees?

Cot 6 degrees is the value of cotangent trigonometric function for an angle equal to 6 degrees. The value of cot 6° is 9.5144 (approx).

What is the Value of Cot 6 Degrees in Terms of Sin 6°?

Using trigonometric identities, we can write cot 6° in terms of sin 6° as, cot(6°) = √(1 - sin²(6°))/sin 6° . Here, the value of sin 6° is equal to 0.1045.

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

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

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

☛ Also check: trigonometric table

What is the Value of Cot 6° in Terms of Cosec 6°?

Since the cotangent function can be represented using the cosecant function, we can write cot 6° as √(cosec²(6°) - 1). The value of cosec 6° is equal to 9.56677.

How to Find the Value of Cot 6 Degrees?

The value of cot 6 degrees can be calculated by constructing an angle of 6° with the x-axis, and then finding the coordinates of the corresponding point (0.9945, 0.1045) on the unit circle. The value of cot 6° is equal to the x-coordinate(0.9945) divided by the y-coordinate (0.1045). ∴ cot 6° = 9.5144