Cot 180 Degrees
The value of cot 180 degrees is undefined. Cot 180 degrees in radians is written as cot (180° × π/180°), i.e., cot (π) or cot (3.141592. . .). In this article, we will discuss the methods to find the value of cot 180 degrees with examples.
 Cot 180°: undefined
 Cot (180 degrees): undefined
 Cot 180° in radians: cot (π) or cot (3.1415926 . . .)
What is the Value of Cot 180 Degrees?
The value of cot 180 degrees is undefined. Cot 180 degrees can also be expressed using the equivalent of the given angle (180 degrees) in radians (3.14159 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 180 degrees = 180° × (π/180°) rad = π or 3.1415 . . .
∴ cot 180° = cot(3.1415) = undefined
Explanation:
For cot 180 degrees, the angle 180° lies on the negative xaxis. Thus, cot 180° value = not defined
Since the cotangent function is a periodic function, we can represent cot 180° as, cot 180 degrees = cot(180° + n × 180°), n ∈ Z.
⇒ cot 180° = cot 360° = cot 540°, and so on.
Methods to Find Value of Cot 180 Degrees
The value of cot 180° is given as "not defined". We can find the value of cot 180 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 180 Degrees Using Unit Circle
To find the value of cot 180 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 180° angle with the positive xaxis.
 The cot of 180 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 180° = x/y = undefined.
Cot 180° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 180 degrees as:
 cos(180°)/sin(180°)
 ± cos 180°/√(1  cos²(180°))
 ± √(1  sin²(180°))/sin 180°
 ± 1/√(sec²(180°)  1)
 ± √(cosec²(180°)  1)
 1/tan 180°
Note: Since 180° lies on the negative xaxis, the final value of cot 180° is undefined.
We can use trigonometric identities to represent cot 180° as,
 tan (90°  180°) = tan(90°)
 tan (90° + 180°) = tan 270°
 cot (180°  180°) = cot 0°
☛ Also Check:
Examples Using Cot 180 Degrees

Example 1: Simplify: 6 (cot 180°/tan(45°))
Solution:
We know cot 180° = undefined and tan(45°) = 1
⇒ 6 (cot 180°/tan(45°)) = undefined 
Example 2: Find the value of cot 180° if tan 180° is 0.
Solution:
Since, cot 180° = 1/tan 180°
⇒ cot 180° = 1/0 = undefined 
Example 3: Find the value of (cos (180°) cosec (90°) sec (90°))/2. [Hint: Use cot 180° = undefined]
Solution:
Using trigonometry formulas,
(cos (180°) cosec (90°) sec (90°))/2 = cos (180°)/(2 sin (90°) cos (90°))
Using sin 2a formula,
2 sin (90°) cos (90°) = sin (2 × 90°) = sin 180°
⇒ cos (180°) / sin (180°) = cot 180°
⇒ (cos (180°) cosec (90°) sec (90°))/2 = undefined
FAQs on Cot 180 Degrees
What is Cot 180 Degrees?
Cot 180 degrees is the value of cotangent trigonometric function for an angle equal to 180 degrees. The value of cot 180° is undefined.
How to Find the Value of Cot 180 Degrees?
The value of cot 180 degrees can be calculated by constructing an angle of 180° with the xaxis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cot 180° is equal to the xcoordinate(1) divided by the ycoordinate (0). ∴ cot 180° = undefined
What is the Exact Value of Cot 180 Degrees?
The exact value of cot 180 degrees is undefined.
What is the Value of Cot 180 Degrees in Terms of Tan 180°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 180° as 1/tan(180°). The value of tan 180° is equal to 0.
How to Find Cot 180° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 180° can be given in terms of other trigonometric functions as:
 cos(180°)/sin(180°)
 ± cos 180°/√(1  cos²(180°))
 ± √(1  sin²(180°))/sin 180°
 ± 1/√(sec²(180°)  1)
 ± √(cosec²(180°)  1)
 1/tan 180°
☛ Also check: trigonometric table
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