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Cot 2pi

The value of cot 2pi is not defined. Cot 2pi radians in degrees is written as cot ((2π) × 180°/π), i.e., cot (360°). In this article, we will discuss the methods to find the value of cot 2pi with examples.

Cot 2pi: not defined
Cot (-2pi): not defined
Cot 2pi in degrees: cot (360°)

What is the Value of Cot 2pi?

The value of cot 2pi is not defined. Cot 2pi can also be expressed using the equivalent of the given angle (2pi) in degrees (360°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 2pi radians = 2pi × (180°/pi) = 360° or 360 degrees
∴ cot 2pi = cot 2π = cot(360°) = not defined

Explanation:

We can represent cot 2pi as, cot(2pi mod 2pi) = cot(0). For cot 2pi, the angle 2pi lies on the positive x-axis. Thus, cot 2pi value = not defined
Since the cotangent function is a periodic function, we can represent cot 2pi as, cot 2pi = cot(2pi + n × pi), n ∈ Z.
⇒ cot 2pi = cot 3pi = cot 4pi , and so on.
Note: Since, cotangent is an odd function, the value of cot(-2pi) = -cot(2pi) = not defined.

Methods to Find Value of Cot 2pi

The value of cot 2pi is given as not defined. We can find the value of cot 2pi by:

Using Unit Circle
Using Trigonometric Functions

Cot 2pi Using Unit Circle

To find the value of cot 2π using the unit circle:

Rotate ‘r’ anticlockwise to form 0 or 2pi angle with the positive x-axis.
The cot of 2pi 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 2pi = x/y = not defined

Cot 2pi in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 2pi as:

cos(2pi)/sin(2pi)
± cos(2pi)/√(1 - cos²(2pi))
± √(1 - sin²(2pi))/sin(2pi)
± 1/√(sec²(2pi) - 1)
± √(cosec²(2pi) - 1)
1/tan(2pi)

Note: Since 2pi lies on the positive x-axis, the final value of cot 2pi is not defined.

We can use trigonometric identities to represent cot 2pi as,

tan (pi/2 - 2pi) = tan(-3pi/2)
-tan (pi/2 + 2pi) = -tan 5pi/2
-cot (pi - 2pi) = -cot(-pi)

☛ Also Check:

Examples Using Cot 2pi

Example 1: Using the value of cot 2pi, solve: (cosec²(2pi) - 1).

Solution:
We know, (cosec²(2pi) - 1) = (cot²(2pi)) = not defined
⇒ (cosec²(2pi) - 1) = not defined
Example 2: Find the value of 2 cot(2pi)/6 cot(pi/4).

Solution:

Using trigonometric identities, we know, cot(2pi) = not defined and cot(pi/4) = 1.
⇒ Value of 2 cot(2pi)/6 cot(pi/4) = not defined
Example 3: Find the value of cot 2pi if tan 2pi is 0.

Solution:
Since, cot 2pi = 1/tan(2pi)
⇒ cot 2pi = 1/0 = not defined

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FAQs on Cot 2pi

What is Cot 2pi?

Cot 2pi is the value of cotangent trigonometric function for an angle equal to 2π radians. The value of cot 2pi is not defined.

What is the Value of Cot 2pi in Terms of Tan 2pi?

Since the cotangent function is the reciprocal of the tangent function, we can write cot 2pi as 1/tan(2pi). The value of tan 2pi is equal to 0.

What is the Exact Value of Cot 2pi?

The exact value of cot 2pi is not defined.

How to Find the Value of Cot 2pi?

The value of cot 2pi can be calculated by constructing an angle of 2π radians with the x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cot 2pi is equal to the x-coordinate(1) divided by the y-coordinate (0). ∴ cot 2pi = not defined

How to Find Cot 2pi in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 2pi can be given in terms of other trigonometric functions as:

cos(2pi)/sin(2pi)
± cos(2pi)/√(1 - cos²(2pi))
± √(1 - sin²(2pi))/sin(2pi)
± 1/√(sec²(2pi) - 1)
± √(cosec²(2pi) - 1)
1/tan(2pi)

☛ Also check: trigonometry table

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