Cot 210 Degrees

The value of cot 210 degrees is 1.7320508. . .. Cot 210 degrees in radians is written as cot (210° × π/180°), i.e., cot (7π/6) or cot (3.665191. . .). In this article, we will discuss the methods to find the value of cot 210 degrees with examples.

• Cot 210°: √3
• Cot 210° in decimal: 1.7320508. . .
• Cot (-210 degrees): -1.7320508. . . or -√3
• Cot 210° in radians: cot (7π/6) or cot (3.6651914 . . .)

What is the Value of Cot 210 Degrees?

The value of cot 210 degrees in decimal is 1.732050807. . .. Cot 210 degrees can also be expressed using the equivalent of the given angle (210 degrees) in radians (3.66519 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 210 degrees = 210° × (π/180°) rad = 7π/6 or 3.6651 . . .
∴ cot 210° = cot(3.6651) = √3 or 1.7320508. . .

Explanation:

For cot 210 degrees, the angle 210° lies between 180° and 270° (Third Quadrant). Since cotangent function is positive in the third quadrant, thus cot 210° value = √3 or 1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot 210° as, cot 210 degrees = cot(210° + n × 180°), n ∈ Z.
⇒ cot 210° = cot 390° = cot 570°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-210°) = -cot(210°).

Methods to Find Value of Cot 210 Degrees

The cotangent function is positive in the 3rd quadrant. The value of cot 210° is given as 1.73205. . . We can find the value of cot 210 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cot 210° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 210 degrees as:

• cos(210°)/sin(210°)
• ± cos 210°/√(1 - cos²(210°))
• ± √(1 - sin²(210°))/sin 210°
• ± 1/√(sec²(210°) - 1)
• ± √(cosec²(210°) - 1)
• 1/tan 210°

Note: Since 210° lies in the 3rd Quadrant, the final value of cot 210° will be positive.

We can use trigonometric identities to represent cot 210° as,

• tan (90° - 210°) = tan(-120°)
• -tan (90° + 210°) = -tan 300°
• -cot (180° - 210°) = -cot(-30°)

Cot 210 Degrees Using Unit Circle

To find the value of cot 210 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 210° angle with the positive x-axis.
• The cot of 210 degrees 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 210° = x/y = 1.7321 (approx).

☛ Also Check:

• cot 3 degrees
• cot 4 degrees
• cot 50 degrees
• cot 9 degrees
• cot 1 degrees
• cot 53 degrees

FAQs on Cot 210 Degrees

What is Cot 210 Degrees?

Cot 210 degrees is the value of cotangent trigonometric function for an angle equal to 210 degrees. The value of cot 210° is √3 or 1.7321 (approx).

How to Find Cot 210° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 210° can be given in terms of other trigonometric functions as:

• cos(210°)/sin(210°)
• ± cos 210°/√(1 - cos²(210°))
• ± √(1 - sin²(210°))/sin 210°
• ± 1/√(sec²(210°) - 1)
• ± √(cosec²(210°) - 1)
• 1/tan 210°

☛ Also check: trigonometric table

What is the Value of Cot 210 Degrees in Terms of Sin 210°?

Using trigonometric identities, we can write cot 210° in terms of sin 210° as, cot(210°) = -√(1 - sin²(210°))/sin 210° . Here, the value of sin 210° is equal to -(1/2).

What is the Exact Value of Cot 210 Degrees?

The exact value of cot 210 degrees can be given accurately up to 8 decimal places as 1.73205080 or as √3.

How to Find the Value of Cot 210 Degrees?

The value of cot 210 degrees can be calculated by constructing an angle of 210° 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 210° is equal to the x-coordinate(-0.866) divided by the y-coordinate (-0.5). ∴ cot 210° = 1.7321