Cot pi/8

The value of cot pi/8 is 2.4142135. . .. Cot pi/8 radians in degrees is written as cot ((π/8) × 180°/π), i.e., cot (22.5°). In this article, we will discuss the methods to find the value of cot pi/8 with examples.

• Cot pi/8 in decimal: 2.4142135. . .
• Cot (-pi/8): -2.4142135. . .
• Cot pi/8 in degrees: cot (22.5°)

What is the Value of Cot pi/8?

The value of cot pi/8 in decimal is 2.414213562. . .. Cot pi/8 can also be expressed using the equivalent of the given angle (pi/8) in degrees (22.5°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/8 radians = pi/8 × (180°/pi) = 22.5° or 22.5 degrees
∴ cot pi/8 = cot π/8 = cot(22.5°) = 2.4142135. . .

Explanation:

For cot pi/8, the angle pi/8 lies between 0 and pi/2 (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot pi/8 value = 2.4142135. . .
Since the cotangent function is a periodic function, we can represent cot pi/8 as, cot pi/8 = cot(pi/8 + n × pi), n ∈ Z.
⇒ cot pi/8 = cot 9pi/8 = cot 17pi/8 , and so on.
Note: Since, cotangent is an odd function, the value of cot(-pi/8) = -cot(pi/8).

Methods to Find Value of Cot pi/8

The cotangent function is positive in the 1st quadrant. The value of cot pi/8 is given as 2.41421. . .. We can find the value of cot pi/8 by:

• Using Trigonometric Functions
• Using Unit Circle

Cot pi/8 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot pi/8 as:

• cos(pi/8)/sin(pi/8)
• ± cos(pi/8)/√(1 - cos²(pi/8))
• ± √(1 - sin²(pi/8))/sin(pi/8)
• ± 1/√(sec²(pi/8) - 1)
• ± √(cosec²(pi/8) - 1)
• 1/tan(pi/8)

Note: Since pi/8 lies in the 1st Quadrant, the final value of cot pi/8 will be positive.

We can use trigonometric identities to represent cot pi/8 as,

• tan (pi/2 - pi/8) = tan 3pi/8
• -tan (pi/2 + pi/8) = -tan 5pi/8
• -cot (pi - pi/8) = -cot 7pi/8

Cot pi/8 Using Unit Circle

To find the value of cot π/8 using the unit circle:

• Rotate ‘r’ anticlockwise to form pi/8 angle with the positive x-axis.
• The cot of pi/8 equals the x-coordinate(0.9239) divided by y-coordinate(0.3827) of the point of intersection (0.9239, 0.3827) of unit circle and r.

Hence the value of cot pi/8 = x/y = 2.4142 (approx)

☛ Also Check:

• sin pi/2
• cos 5pi/3
• sin 5pi/8
• csc pi/6
• cos 11pi/6
• cot 5pi/4

FAQs on Cot pi/8

What is Cot pi/8?

Cot pi/8 is the value of cotangent trigonometric function for an angle equal to π/8 radians. The value of cot pi/8 is 2.4142 (approx).

How to Find the Value of Cot pi/8?

The value of cot pi/8 can be calculated by constructing an angle of π/8 radians with the x-axis, and then finding the coordinates of the corresponding point (0.9239, 0.3827) on the unit circle. The value of cot pi/8 is equal to the x-coordinate(0.9239) divided by the y-coordinate (0.3827). ∴ cot pi/8 = 2.4142

What is the Value of Cot pi/8 in Terms of Sin pi/8?

Using trigonometric identities, we can write cot pi/8 in terms of sin pi/8 as, cot(pi/8) = √(1 - sin²(pi/8))/sin pi/8 . Here, the value of sin pi/8 is equal to 0.3827.

What is the Exact Value of Cot pi/8?

The exact value of cot pi/8 can be given accurately up to 8 decimal places as 2.41421356.

How to Find Cot pi/8 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot pi/8 can be given in terms of other trigonometric functions as:

• cos(pi/8)/sin(pi/8)
• ± cos(pi/8)/√(1 - cos²(pi/8))
• ± √(1 - sin²(pi/8))/sin(pi/8)
• ± 1/√(sec²(pi/8) - 1)
• ± √(cosec²(pi/8) - 1)
• 1/tan(pi/8)

☛ Also check: trigonometry table