Cot 360 Degrees
The value of cot 360 degrees is ∞. Cot 360 degrees in radians is written as cot (360° × π/180°), i.e., cot (2π) or cot (6.283185. . .). In this article, we will discuss the methods to find the value of cot 360 degrees with examples.
 Cot 360°: undefined(∞)
 Cot 360° in radians: cot (2π) or cot (6.2831853 . . .)
What is the Value of Cot 360 Degrees?
The value of cot 360 degrees is ∞. Cot 360 degrees can also be expressed using the equivalent of the given angle (360 degrees) in radians (6.28318 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 360 degrees = 360° × (π/180°) rad = 2π or 6.2831 . . .
∴ cot 360° = cot(6.2831) = undefined(∞)
Explanation:
For cot 360 degrees, the angle 360° lies on the positive xaxis. Thus cot 360° value = undefined(∞)
Since the cotangent function is a periodic function, we can represent cot 360° as, cot 360 degrees = cot(360° + n × 180°), n ∈ Z.
⇒ cot 360° = cot 540° = cot 720°, and so on.
Methods to Find Value of Cot 360 Degrees
The value of cot 360° is given as undefined(∞). We can find the value of cot 360 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 360° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 360 degrees as:
 cos(360°)/sin(360°)
 ± cos 360°/√(1  cos²(360°))
 ± √(1  sin²(360°))/sin 360°
 ± 1/√(sec²(360°)  1)
 ± √(cosec²(360°)  1)
 1/tan 360°
We can use trigonometric identities to represent cot 360° as,
 tan (90°  360°) = tan(270°)
 tan (90° + 360°) = tan 450°
 cot (180°  360°) = cot(180°)
Note: Since 360° lies on the positive xaxis, the final value of cot 360° is undefined.
Cot 360 Degrees Using Unit Circle
To find the value of cot 360 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 0° or 360° angle with the positive xaxis.
 The cot of 360 degrees equals the xcoordinate(1) divided by ycoordinate(0) of the point of intersection (1, 0) of unit circle and r.
Hence the value of cot 360° = x/y = undefined(∞).
☛ Also Check:
Examples Using Cot 360 Degrees

Example 1: Find the value of (cos (360°) cosec (180°) sec (180°))/2. [Hint: Use cot 360° = undefined(∞)]
Solution:
Using trigonometry formulas,
(cos (360°) cosec (180°) sec (180°))/2 = cos (360°)/(2 sin (180°) cos (180°))
Using sin 2a formula,
2 sin (180°) cos (180°) = sin (2 × 180°) = sin 360°
⇒ cos (360°) / sin (360°) = cot 360°
⇒ (cos (360°) cosec (180°) sec (180°))/2 = undefined(∞) 
Example 2: Using the value of cot 360°, solve: (cosec²(360°)  1).
Solution:
We know, (cosec²(360°)  1) = (cot²(360°)) = undefined 
Example 3: Find the value of cot 360° if tan 360° is 0.
Solution:
Since, cot 360° = 1/tan 360°
⇒ cot 360° = 1/0 = undefined(∞)
FAQs on Cot 360 Degrees
What is Cot 360 Degrees?
Cot 360 degrees is the value of cotangent trigonometric function for an angle equal to 360 degrees. The value of cot 360° is undefined(∞).
What is the Value of Cot 360° in Terms of Cosec 360°?
Since the cotangent function can be represented using the cosecant function, we can write cot 360° as √(cosec²(360°)  1). The value of cosec 360° is undefined(∞).
How to Find the Value of Cot 360 Degrees?
The value of cot 360 degrees can be calculated by constructing an angle of 360° with the xaxis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cot 360° is equal to the xcoordinate(1) divided by the ycoordinate (0). ∴ cot 360° = undefined(∞)
What is the Value of Cot 360 Degrees in Terms of Sin 360°?
Using trigonometric identities, we can write cot 360° in terms of sin 360° as, cot(360°) = √(1  sin²(360°))/sin 360° . Here, the value of sin 360° is equal to 0.
How to Find Cot 360° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 360° can be given in terms of other trigonometric functions as:
 cos(360°)/sin(360°)
 ± cos 360°/√(1  cos²(360°))
 ± √(1  sin²(360°))/sin 360°
 ± 1/√(sec²(360°)  1)
 ± √(cosec²(360°)  1)
 1/tan 360°
☛ Also check: trigonometric table
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