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 x-axis. 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 x-axis, 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 x-axis.
• The cot of 360 degrees equals the x-coordinate(1) divided by y-coordinate(0) of the point of intersection (1, 0) of unit circle and r.

Hence the value of cot 360° = x/y = undefined(∞).

☛ Also Check:

• cot 238 degrees
• cot 20 degrees
• cot 30 degrees
• cot 765 degrees
• cot 12 degrees
• cot 240 degrees

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 x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cot 360° is equal to the x-coordinate(1) divided by the y-coordinate (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