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Cot 3pi/4
The value of cot 3pi/4 is 1. Cot 3pi/4 radians in degrees is written as cot ((3π/4) × 180°/π), i.e., cot (135°). In this article, we will discuss the methods to find the value of cot 3pi/4 with examples.
 Cot 3pi/4: 1
 Cot (3pi/4): 1
 Cot 3pi/4 in degrees: cot (135°)
What is the Value of Cot 3pi/4?
The value of cot 3pi/4 is 1. Cot 3pi/4 can also be expressed using the equivalent of the given angle (3pi/4) in degrees (135°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 3pi/4 radians = 3pi/4 × (180°/pi) = 135° or 135 degrees
∴ cot 3pi/4 = cot 3π/4 = cot(135°) = 1
Explanation:
For cot 3pi/4, the angle 3pi/4 lies between pi/2 and pi (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 3pi/4 value = 1
Since the cotangent function is a periodic function, we can represent cot 3pi/4 as, cot 3pi/4 = cot(3pi/4 + n × pi), n ∈ Z.
⇒ cot 3pi/4 = cot 7pi/4 = cot 11pi/4 , and so on.
Note: Since, cotangent is an odd function, the value of cot(3pi/4) = cot(3pi/4).
Methods to Find Value of Cot 3pi/4
The cotangent function is negative in the 2nd quadrant. The value of cot 3pi/4 is given as 1. We can find the value of cot 3pi/4 by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 3pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 3pi/4 as:
 cos(3pi/4)/sin(3pi/4)
 ± cos(3pi/4)/√(1  cos²(3pi/4))
 ± √(1  sin²(3pi/4))/sin(3pi/4)
 ± 1/√(sec²(3pi/4)  1)
 ± √(cosec²(3pi/4)  1)
 1/tan(3pi/4)
Note: Since 3pi/4 lies in the 2nd Quadrant, the final value of cot 3pi/4 will be negative.
We can use trigonometric identities to represent cot 3pi/4 as,
 tan (pi/2  3pi/4) = tan(pi/4)
 tan (pi/2 + 3pi/4) = tan 5pi/4
 cot (pi  3pi/4) = cot pi/4
Cot 3pi/4 Using Unit Circle
To find the value of cot 3π/4 using the unit circle:
 Rotate ‘r’ anticlockwise to form 3pi/4 angle with the positive xaxis.
 The cot of 3pi/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 3pi/4 = x/y = 1
☛ Also Check:
Examples Using Cot 3pi/4

Example 1: Find the value of 4 cot(3pi/4)/5 cot(pi/4).
Solution:
Using trigonometric identities, we know, cot(3pi/4) = cot(pi  3pi/4) = cot pi/4.
⇒ cot(3pi/4) = cot(pi/4)
⇒ Value of 4 cot(3pi/4)/5 cot(pi/4) = 4/5 
Example 2: Simplify: 7 (cot(3pi/4)/tan(pi/4))
Solution:
We know cot 3pi/4 = tan(pi/4)
⇒ 7 cot(3pi/4)/tan(pi/4) = 7 (cot(3pi/4)/cot(3pi/4))
= 7(1) = 7 
Example 3: Find the value of (cos (3pi/4) cosec (3pi/8) sec (3pi/8))/2. [Hint: Use cot 3pi/4 = 1]
Solution:
Using trigonometry formulas,
(cos (3pi/4) cosec (3pi/8) sec (3pi/8))/2 = cos (3pi/4)/(2 sin (3pi/8) cos (3pi/8))
Using sin 2a formula,
2 sin (3pi/8) cos (3pi/8) = sin (2 × 3pi/8) = sin 3pi/4
⇒ cos (3pi/4) / sin (3pi/4) = cot 3pi/4
⇒ (cos (3pi/4) cosec (3pi/8) sec (3pi/8))/2 = 1
FAQs on Cot 3pi/4
What is Cot 3pi/4?
Cot 3pi/4 is the value of cotangent trigonometric function for an angle equal to 3π/4 radians. The value of cot 3pi/4 is 1.
What is the Value of Cot 3pi/4 in Terms of Cosec 3pi/4?
Since the cotangent function can be represented using the cosecant function, we can write cot 3pi/4 as √(cosec²(3pi/4)  1). The value of cosec 3pi/4 is equal to 1.41421.
What is the Value of Cot 3pi/4 in Terms of Cos 3pi/4?
We know, using trig identities, we can write cot 3pi/4 as cos(3pi/4)/√(1  cos²(3pi/4)). Here, the value of cos 3pi/4 is equal to 0.707106.
How to Find the Value of Cot 3pi/4?
The value of cot 3pi/4 can be calculated by constructing an angle of 3π/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 3pi/4 is equal to the xcoordinate(0.7071) divided by the ycoordinate (0.7071). ∴ cot 3pi/4 = 1
How to Find Cot 3pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 3pi/4 can be given in terms of other trigonometric functions as:
 cos(3pi/4)/sin(3pi/4)
 ± cos(3pi/4)/√(1  cos²(3pi/4))
 ± √(1  sin²(3pi/4))/sin(3pi/4)
 ± 1/√(sec²(3pi/4)  1)
 ± √(cosec²(3pi/4)  1)
 1/tan(3pi/4)
☛ Also check: trigonometry table
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