Cot 3pi/2
The value of cot 3pi/2 is 0. Cot 3pi/2 radians in degrees is written as cot ((3π/2) × 180°/π), i.e., cot (270°). In this article, we will discuss the methods to find the value of cot 3pi/2 with examples.
 Cot 3pi/2: 0
 Cot (3pi/2): 0
 Cot 3pi/2 in degrees: cot (270°)
What is the Value of Cot 3pi/2?
The value of cot 3pi/2 is 0. Cot 3pi/2 can also be expressed using the equivalent of the given angle (3pi/2) in degrees (270°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 3pi/2 radians = 3pi/2 × (180°/pi) = 270° or 270 degrees
∴ cot 3pi/2 = cot 3π/2 = cot(270°) = 0
Explanation:
For cot 3pi/2, the angle 3pi/2 lies on the negative yaxis. Thus, cot 3pi/2 value = 0
Since the cotangent function is a periodic function, we can represent cot 3pi/2 as, cot 3pi/2 = cot(3pi/2 + n × pi), n ∈ Z.
⇒ cot 3pi/2 = cot 5pi/2 = cot 7pi/2 , and so on.
Note: Since, cotangent is an odd function, the value of cot(3pi/2) = cot(3pi/2) = 0.
Methods to Find Value of Cot 3pi/2
The value of cot 3pi/2 is given as 0. We can find the value of cot 3pi/2 by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 3pi/2 Using Unit Circle
To find the value of cot 3π/2 using the unit circle:
 Rotate ‘r’ anticlockwise to form 3pi/2 angle with the positive xaxis.
 The cot of 3pi/2 equals the xcoordinate(0) divided by ycoordinate(1) of the point of intersection (0, 1) of unit circle and r.
Hence the value of cot 3pi/2 = x/y = 0
Cot 3pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 3pi/2 as:
 cos(3pi/2)/sin(3pi/2)
 ± cos(3pi/2)/√(1  cos²(3pi/2))
 ± √(1  sin²(3pi/2))/sin(3pi/2)
 ± 1/√(sec²(3pi/2)  1)
 ± √(cosec²(3pi/2)  1)
 1/tan(3pi/2)
Note: Since 3pi/2 lies on the negative yaxis, the final value of cot 3pi/2 is 0.
We can use trigonometric identities to represent cot 3pi/2 as,
 tan (pi/2  3pi/2) = tan(pi)
 tan (pi/2 + 3pi/2) = tan 2pi
 cot (pi  3pi/2) = cot(pi/2)
☛ Also Check:
Examples Using Cot 3pi/2

Example 1: Find the value of (cos (3pi/2) cosec (3pi/4) sec (3pi/4))/2. [Hint: Use cot 3pi/2 = 0]
Solution:
Using trigonometry formulas,
(cos (3pi/2) cosec (3pi/4) sec (3pi/4))/2 = cos (3pi/2)/(2 sin (3pi/4) cos (3pi/4))
Using sin 2a formula,
2 sin (3pi/4) cos (3pi/4) = sin (2 × 3pi/4) = sin 3pi/2
⇒ cos (3pi/2) / sin (3pi/2) = cot 3pi/2
⇒ (cos (3pi/2) cosec (3pi/4) sec (3pi/4))/2 = 0 
Example 2: Find the value of 6 cot(3pi/2)/8 cot(pi/4).
Solution:
Using trigonometric values, we know, cot(3pi/2) = 0 and cot(pi/4) = 1.
⇒ Value of 6 cot(3pi/2)/8 cot(pi/4) = 0 
Example 3: Simplify: 3 (cot(3pi/2)/tan(pi/4))
Solution:
We know cot 3pi/2 = 0 and tan(pi/4) = 1
⇒ 3 cot(3pi/2)/tan(pi/4) = 0
FAQs on Cot 3pi/2
What is Cot 3pi/2?
Cot 3pi/2 is the value of cotangent trigonometric function for an angle equal to 3π/2 radians. The value of cot 3pi/2 is 0.
How to Find Cot 3pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 3pi/2 can be given in terms of other trigonometric functions as:
 cos(3pi/2)/sin(3pi/2)
 ± cos(3pi/2)/√(1  cos²(3pi/2))
 ± √(1  sin²(3pi/2))/sin(3pi/2)
 ± 1/√(sec²(3pi/2)  1)
 ± √(cosec²(3pi/2)  1)
 1/tan(3pi/2)
☛ Also check: trigonometry table
What is the Value of Cot 3pi/2 in Terms of Sec 3pi/2?
We can represent the cotangent function in terms of the secant function using trig identities, cot 3pi/2 can be written as 1/√(sec²(3pi/2)  1).
What is the Value of Cot 3pi/2 in Terms of Cos 3pi/2?
We know, using trig identities, we can write cot 3pi/2 as cos(3pi/2)/√(1  cos²(3pi/2)). Here, the value of cos 3pi/2 is equal to 0.
How to Find the Value of Cot 3pi/2?
The value of cot 3pi/2 can be calculated by constructing an angle of 3π/2 radians with the xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cot 3pi/2 is equal to the xcoordinate(0) divided by the ycoordinate (1). ∴ cot 3pi/2 = 0
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