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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 xaxis.
 The cot of pi/8 equals the xcoordinate(0.9239) divided by ycoordinate(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:
Examples Using Cot pi/8

Example 1: Find the value of (cos (pi/8) cosec (pi/16) sec (pi/16))/2. [Hint: Use cot pi/8 = 2.4142]
Solution:
Using trigonometry formulas,
(cos (pi/8) cosec (pi/16) sec (pi/16))/2 = cos (pi/8)/(2 sin (pi/16) cos (pi/16))
Using sin 2a formula,
2 sin (pi/16) cos (pi/16) = sin (2 × pi/16) = sin pi/8
⇒ cos (pi/8) / sin (pi/8) = cot pi/8
⇒ (cos (pi/8) cosec (pi/16) sec (pi/16))/2 = 2.4142 
Example 2: Find the value of 3 cot(pi/8)/10 cot(7pi/8).
Solution:
Using trigonometric identities, we know, cot(pi/8) = cot(pi  pi/8) = cot 7pi/8.
⇒ cot(pi/8) = cot(7pi/8)
⇒ Value of 3 cot(pi/8)/10 cot(7pi/8) = 3/10 
Example 3: Using the value of cot pi/8, solve: (cosec²(pi/8)  1).
Solution:
We know, (cosec²(pi/8)  1) = (cot²(pi/8)) = 5.8284
⇒ (cosec²(pi/8)  1) = 5.8284
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 xaxis, 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 xcoordinate(0.9239) divided by the ycoordinate (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
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