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Cot 330 Degrees
The value of cot 330 degrees is 1.7320508. . .. Cot 330 degrees in radians is written as cot (330° × π/180°), i.e., cot (11π/6) or cot (5.759586. . .). In this article, we will discuss the methods to find the value of cot 330 degrees with examples.
 Cot 330°: √3
 Cot 330° in decimal: 1.7320508. . .
 Cot (330 degrees): 1.7320508. . . or √3
 Cot 330° in radians: cot (11π/6) or cot (5.7595865 . . .)
What is the Value of Cot 330 Degrees?
The value of cot 330 degrees in decimal is 1.732050807. . .. Cot 330 degrees can also be expressed using the equivalent of the given angle (330 degrees) in radians (5.75958 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 330 degrees = 330° × (π/180°) rad = 11π/6 or 5.7595 . . .
∴ cot 330° = cot(5.7595) = √3 or 1.7320508. . .
Explanation:
For cot 330 degrees, the angle 330° lies between 270° and 360° (Fourth Quadrant). Since cotangent function is negative in the fourth quadrant, thus cot 330° value = √3 or 1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot 330° as, cot 330 degrees = cot(330° + n × 180°), n ∈ Z.
⇒ cot 330° = cot 510° = cot 690°, and so on.
Note: Since, cotangent is an odd function, the value of cot(330°) = cot(330°).
Methods to Find Value of Cot 330 Degrees
The cotangent function is negative in the 4th quadrant. The value of cot 330° is given as 1.73205. . . We can find the value of cot 330 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 330 Degrees Using Unit Circle
To find the value of cot 330 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 330° angle with the positive xaxis.
 The cot of 330 degrees equals the xcoordinate(0.866) divided by ycoordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of cot 330° = x/y = 1.7321 (approx).
Cot 330° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 330 degrees as:
 cos(330°)/sin(330°)
 ± cos 330°/√(1  cos²(330°))
 ± √(1  sin²(330°))/sin 330°
 ± 1/√(sec²(330°)  1)
 ± √(cosec²(330°)  1)
 1/tan 330°
Note: Since 330° lies in the 4th Quadrant, the final value of cot 330° will be negative.
We can use trigonometric identities to represent cot 330° as,
 tan (90°  330°) = tan(240°)
 tan (90° + 330°) = tan 420°
 cot (180°  330°) = cot(150°)
☛ Also Check:
Examples Using Cot 330 Degrees

Example 1: Using the value of cot 330°, solve: (cosec²(330°)  1).
Solution:
We know, (cosec²(330°)  1) = (cot²(330°)) = 3
⇒ (cosec²(330°)  1) = 3 
Example 2: Find the value of (cos (330°) cosec (165°) sec (165°))/2. [Hint: Use cot 330° = 1.7321]
Solution:
Using trigonometry formulas,
(cos (330°) cosec (165°) sec (165°))/2 = cos (330°)/(2 sin (165°) cos (165°))
Using sin 2a formula,
2 sin (165°) cos (165°) = sin (2 × 165°) = sin 330°
⇒ cos (330°) / sin (330°) = cot 330°
⇒ (cos (330°) cosec (165°) sec (165°))/2 = 1.7321 
Example 3: Find the value of 3 cot(330°)/8 cot(150°).
Solution:
Using trigonometric identities, we know, cot(330°) = cot(180°  330°) = cot(150°).
⇒ cot(330°) = cot(150°)
⇒ Value of 3 cot(330°)/8 cot(150°) = 3/8
FAQs on Cot 330 Degrees
What is Cot 330 Degrees?
Cot 330 degrees is the value of cotangent trigonometric function for an angle equal to 330 degrees. The value of cot 330° is √3 or 1.7321 (approx).
How to Find the Value of Cot 330 Degrees?
The value of cot 330 degrees can be calculated by constructing an angle of 330° with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cot 330° is equal to the xcoordinate(0.866) divided by the ycoordinate (0.5). ∴ cot 330° = 1.7321
What is the Exact Value of Cot 330 Degrees?
The exact value of cot 330 degrees can be given accurately up to 8 decimal places as 1.73205080 or as √3.
What is the Value of Cot 330 Degrees in Terms of Sin 330°?
Using trigonometric identities, we can write cot 330° in terms of sin 330° as, cot(330°) = √(1  sin²(330°))/sin 330° . Here, the value of sin 330° is equal to (1/2).
How to Find Cot 330° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 330° can be given in terms of other trigonometric functions as:
 cos(330°)/sin(330°)
 ± cos 330°/√(1  cos²(330°))
 ± √(1  sin²(330°))/sin 330°
 ± 1/√(sec²(330°)  1)
 ± √(cosec²(330°)  1)
 1/tan 330°
☛ Also check: trigonometry table
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