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Cot pi
The value of cot pi is not defined. Cot pi radians in degrees is written as cot ((π) × 180°/π), i.e., cot (180°). In this article, we will discuss the methods to find the value of cot pi with examples.
 Cot pi: not defined
 Cot (pi): not defined
 Cot pi in degrees: cot (180°)
What is the Value of Cot pi?
The value of cot pi is not defined. Cot pi can also be expressed using the equivalent of the given angle (pi) in degrees (180°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi radians = pi × (180°/pi) = 180° or 180 degrees
∴ cot pi = cot π = cot(180°) = not defined
Explanation:
For cot pi, the angle pi lies on the negative xaxis. Thus, cot pi value = not defined
Since the cotangent function is a periodic function, we can represent cot pi as, cot pi = cot(pi + n × pi), n ∈ Z.
⇒ cot pi = cot 2pi = cot 3pi , and so on.
Note: Since, cotangent is an odd function, the value of cot(pi) = cot(pi) = not defined.
Methods to Find Value of Cot pi
The value of cot pi is given as not defined. We can find the value of cot pi by:
 Using Trigonometric Functions
 Using Unit Circle
Cot pi in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot pi as:
 cos(pi)/sin(pi)
 ± cos(pi)/√(1  cos²(pi))
 ± √(1  sin²(pi))/sin(pi)
 ± 1/√(sec²(pi)  1)
 ± √(cosec²(pi)  1)
 1/tan(pi)
Note: Since pi lies on the negative xaxis, the final value of cot pi is not defined.
We can use trigonometric identities to represent cot pi as,
 tan (pi/2  pi) = tan(pi/2)
 tan (pi/2 + pi) = tan 3pi/2
 cot (pi  pi) = cot 0
Cot pi Using Unit Circle
To find the value of cot π using the unit circle:
 Rotate ‘r’ anticlockwise to form pi angle with the positive xaxis.
 The cot of pi 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 pi = x/y = not defined
☛ Also Check:
Examples Using Cot pi

Example 1: Simplify: 8 (cot(pi)/tan(pi/4))
Solution:
We know cot pi = not defined and tan(pi/4) = 1
⇒ 8 cot(pi)/tan(pi/4) = not defined 
Example 2: Find the value of cot pi if tan pi is 0.
Solution:
Since, cot pi = 1/tan(pi)
⇒ cot pi = 1/0 = not defined 
Example 3: Find the value of 6 cot(pi)/8 cot(pi/4).
Solution:
Using trigonometric values, we know, cot(pi) = not defined and cot(pi/4) = 1
⇒ Value of 6 cot(pi)/8 cot(pi/4) = not defined
FAQs on Cot pi
What is Cot pi?
Cot pi is the value of cotangent trigonometric function for an angle equal to π radians. The value of cot pi is not defined.
What is the Value of Cot pi in Terms of Sin pi?
Using trigonometric identities, we can write cot pi in terms of sin pi as, cot(pi) = √(1  sin²(pi))/sin pi . Here, the value of sin pi is equal to 0.
How to Find the Value of Cot pi?
The value of cot pi can be calculated by constructing an angle of π radians with the xaxis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cot pi is equal to the xcoordinate(1) divided by the ycoordinate (0). ∴ cot pi = not defined
How to Find Cot pi in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot pi can be given in terms of other trigonometric functions as:
 cos(pi)/sin(pi)
 ± cos(pi)/√(1  cos²(pi))
 ± √(1  sin²(pi))/sin(pi)
 ± 1/√(sec²(pi)  1)
 ± √(cosec²(pi)  1)
 1/tan(pi)
☛ Also check: trigonometric table
What is the Value of Cot pi in Terms of Sec pi?
We can represent the cotangent function in terms of the secant function using trig identities, cot pi can be written as 1/√(sec²(pi)  1). Here, the value of sec pi is equal to 1.
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