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Cot pi/4
The value of cot pi/4 is 1. Cot pi/4 radians in degrees is written as cot ((π/4) × 180°/π), i.e., cot (45°). In this article, we will discuss the methods to find the value of cot pi/4 with examples.
 Cot pi/4: 1
 Cot (pi/4): 1
 Cot pi/4 in degrees: cot (45°)
What is the Value of Cot pi/4?
The value of cot pi/4 is 1. Cot pi/4 can also be expressed using the equivalent of the given angle (pi/4) in degrees (45°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/4 radians = pi/4 × (180°/pi) = 45° or 45 degrees
∴ cot pi/4 = cot π/4 = cot(45°) = 1
Explanation:
For cot pi/4, the angle pi/4 lies between 0 and pi/2 (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot pi/4 value = 1
Since the cotangent function is a periodic function, we can represent cot pi/4 as, cot pi/4 = cot(pi/4 + n × pi), n ∈ Z.
⇒ cot pi/4 = cot 5pi/4 = cot 9pi/4 , and so on.
Note: Since, cotangent is an odd function, the value of cot(pi/4) = cot(pi/4).
Methods to Find Value of Cot pi/4
The cotangent function is positive in the 1st quadrant. The value of cot pi/4 is given as 1. We can find the value of cot pi/4 by:
 Using Trigonometric Functions
 Using Unit Circle
Cot pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot pi/4 as:
 cos(pi/4)/sin(pi/4)
 ± cos(pi/4)/√(1  cos²(pi/4))
 ± √(1  sin²(pi/4))/sin(pi/4)
 ± 1/√(sec²(pi/4)  1)
 ± √(cosec²(pi/4)  1)
 1/tan(pi/4)
Note: Since pi/4 lies in the 1st Quadrant, the final value of cot pi/4 will be positive.
We can use trigonometric identities to represent cot pi/4 as,
 tan (pi/2  pi/4) = tan pi/4
 tan (pi/2 + pi/4) = tan 3pi/4
 cot (pi  pi/4) = cot 3pi/4
Cot pi/4 Using Unit Circle
To find the value of cot π/4 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/4 angle with the positive xaxis.
 The cot of pi/4 equals the xcoordinate(0.7071) divided by ycoordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.
Hence the value of cot pi/4 = x/y = 1
☛ Also Check:
Examples Using Cot pi/4

Example 1: Find the value of cot pi/4 if tan pi/4 is 1.
Solution:
Since, cot pi/4 = 1/tan(pi/4)
⇒ cot pi/4 = 1/1 = 1 
Example 2: Using the value of cot pi/4, solve: (cosec²(pi/4)  1).
Solution:
We know, (cosec²(pi/4)  1) = (cot²(pi/4)) = 1
⇒ (cosec²(pi/4)  1) = 1 
Example 3: Find the value of (cos (pi/4) cosec (pi/8) sec (pi/8))/2. [Hint: Use cot pi/4 = 1]
Solution:
Using trigonometry formulas,
(cos (pi/4) cosec (pi/8) sec (pi/8))/2 = cos (pi/4)/(2 sin (pi/8) cos (pi/8))
Using sin 2a formula,
2 sin (pi/8) cos (pi/8) = sin (2 × pi/8) = sin pi/4
⇒ cos (pi/4) / sin (pi/4) = cot pi/4
⇒ (cos (pi/4) cosec (pi/8) sec (pi/8))/2 = 1
FAQs on Cot pi/4
What is Cot pi/4?
Cot pi/4 is the value of cotangent trigonometric function for an angle equal to π/4 radians. The value of cot pi/4 is 1.
How to Find the Value of Cot pi/4?
The value of cot pi/4 can be calculated by constructing an angle of π/4 radians with the xaxis, and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of cot pi/4 is equal to the xcoordinate(0.7071) divided by the ycoordinate (0.7071). ∴ cot pi/4 = 1
How to Find Cot pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot pi/4 can be given in terms of other trigonometric functions as:
 cos(pi/4)/sin(pi/4)
 ± cos(pi/4)/√(1  cos²(pi/4))
 ± √(1  sin²(pi/4))/sin(pi/4)
 ± 1/√(sec²(pi/4)  1)
 ± √(cosec²(pi/4)  1)
 1/tan(pi/4)
☛ Also check: trigonometric table
What is the Value of Cot pi/4 in Terms of Tan pi/4?
Since the cotangent function is the reciprocal of the tangent function, we can write cot pi/4 as 1/tan(pi/4). The value of tan pi/4 is equal to 1.
What is the Exact Value of Cot pi/4?
The exact value of cot pi/4 is 1.
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