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 x-axis. 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 x-axis, 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 x-axis.
• The cot of pi 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 pi = x/y = not defined

☛ Also Check:

• sin 3pi/4
• tan pi
• sin 3pi/2
• cos pi/3
• cos 17pi/12
• sin 7pi/12

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