Cot 5pi/4
The value of cot 5pi/4 is 1. Cot 5pi/4 radians in degrees is written as cot ((5π/4) × 180°/π), i.e., cot (225°). In this article, we will discuss the methods to find the value of cot 5pi/4 with examples.
 Cot 5pi/4: 1
 Cot (5pi/4): 1
 Cot 5pi/4 in degrees: cot (225°)
What is the Value of Cot 5pi/4?
The value of cot 5pi/4 is 1. Cot 5pi/4 can also be expressed using the equivalent of the given angle (5pi/4) in degrees (225°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/4 radians = 5pi/4 × (180°/pi) = 225° or 225 degrees
∴ cot 5pi/4 = cot 5π/4 = cot(225°) = 1
Explanation:
For cot 5pi/4, the angle 5pi/4 lies between pi and 3pi/2 (Third Quadrant). Since cotangent function is positive in the third quadrant, thus cot 5pi/4 value = 1
Since the cotangent function is a periodic function, we can represent cot 5pi/4 as, cot 5pi/4 = cot(5pi/4 + n × pi), n ∈ Z.
⇒ cot 5pi/4 = cot 9pi/4 = cot 13pi/4 , and so on.
Note: Since, cotangent is an odd function, the value of cot(5pi/4) = cot(5pi/4).
Methods to Find Value of Cot 5pi/4
The cotangent function is positive in the 3rd quadrant. The value of cot 5pi/4 is given as 1. We can find the value of cot 5pi/4 by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 5pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 5pi/4 as:
 cos(5pi/4)/sin(5pi/4)
 ± cos(5pi/4)/√(1  cos²(5pi/4))
 ± √(1  sin²(5pi/4))/sin(5pi/4)
 ± 1/√(sec²(5pi/4)  1)
 ± √(cosec²(5pi/4)  1)
 1/tan(5pi/4)
Note: Since 5pi/4 lies in the 3rd Quadrant, the final value of cot 5pi/4 will be positive.
We can use trigonometric identities to represent cot 5pi/4 as,
 tan (pi/2  5pi/4) = tan(3pi/4)
 tan (pi/2 + 5pi/4) = tan 7pi/4
 cot (pi  5pi/4) = cot(pi/4)
Cot 5pi/4 Using Unit Circle
To find the value of cot 5π/4 using the unit circle:
 Rotate ‘r’ anticlockwise to form 5pi/4 angle with the positive xaxis.
 The cot of 5pi/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 5pi/4 = x/y = 1
☛ Also Check:
Examples Using Cot 5pi/4

Example 1: Using the value of cot 5pi/4, solve: (cosec²(5pi/4)  1).
Solution:
We know, (cosec²(5pi/4)  1) = (cot²(5pi/4)) = 1
⇒ (cosec²(5pi/4)  1) = 1 
Example 2: Find the value of 9 cot(5pi/4)/10 cot(pi/4).
Solution:
Using trigonometric identities, we know, cot(5pi/4) = cot(pi  5pi/4) = cot(pi/4).
⇒ cot(5pi/4) = cot(pi/4)
⇒ Value of 9 cot(5pi/4)/10 cot(pi/4) = 9/10 
Example 3: Find the value of cot 5pi/4 if tan 5pi/4 is 1.
Solution:
Since, cot 5pi/4 = 1/tan(5pi/4)
⇒ cot 5pi/4 = 1/1 = 1
FAQs on Cot 5pi/4
What is Cot 5pi/4?
Cot 5pi/4 is the value of cotangent trigonometric function for an angle equal to 5π/4 radians. The value of cot 5pi/4 is 1.
What is the Value of Cot 5pi/4 in Terms of Sec 5pi/4?
We can represent the cotangent function in terms of the secant function using trig identities, cot 5pi/4 can be written as 1/√(sec²(5pi/4)  1). Here, the value of sec 5pi/4 is equal to 1.4142.
How to Find Cot 5pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 5pi/4 can be given in terms of other trigonometric functions as:
 cos(5pi/4)/sin(5pi/4)
 ± cos(5pi/4)/√(1  cos²(5pi/4))
 ± √(1  sin²(5pi/4))/sin(5pi/4)
 ± 1/√(sec²(5pi/4)  1)
 ± √(cosec²(5pi/4)  1)
 1/tan(5pi/4)
☛ Also check: trigonometric table
How to Find the Value of Cot 5pi/4?
The value of cot 5pi/4 can be calculated by constructing an angle of 5π/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 5pi/4 is equal to the xcoordinate(0.7071) divided by the ycoordinate (0.7071). ∴ cot 5pi/4 = 1
What is the Value of Cot 5pi/4 in Terms of Cos 5pi/4?
We know, using trig identities, we can write cot 5pi/4 as cos(5pi/4)/√(1  cos²(5pi/4)). Here, the value of cos 5pi/4 is equal to 0.707106.
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