Cot pi/2
The value of cot pi/2 is 0. Cot pi/2 radians in degrees is written as cot ((π/2) × 180°/π), i.e., cot (90°). In this article, we will discuss the methods to find the value of cot pi/2 with examples.
 Cot pi/2: 0
 Cot (pi/2): 0
 Cot pi/2 in degrees: cot (90°)
What is the Value of Cot pi/2?
The value of cot pi/2 is 0. Cot pi/2 can also be expressed using the equivalent of the given angle (pi/2) in degrees (90°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/2 radians = pi/2 × (180°/pi) = 90° or 90 degrees
∴ cot pi/2 = cot π/2 = cot(90°) = 0
Explanation:
For cot pi/2, the angle pi/2 lies on the positive yaxis. Thus, cot pi/2 value = 0
Since the cotangent function is a periodic function, we can represent cot pi/2 as, cot pi/2 = cot(pi/2 + n × pi), n ∈ Z.
⇒ cot pi/2 = cot 3pi/2 = cot 5pi/2 , and so on.
Note: Since, cotangent is an odd function, the value of cot(pi/2) = cot(pi/2) = 0.
Methods to Find Value of Cot pi/2
The value of cot pi/2 is given as 0. We can find the value of cot pi/2 by:
 Using Unit Circle
 Using Trigonometric Functions
Cot pi/2 Using Unit Circle
To find the value of cot π/2 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/2 angle with the positive xaxis.
 The cot of pi/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 pi/2 = x/y = 0
Cot pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot pi/2 as:
 cos(pi/2)/sin(pi/2)
 ± cos(pi/2)/√(1  cos²(pi/2))
 ± √(1  sin²(pi/2))/sin(pi/2)
 ± 1/√(sec²(pi/2)  1)
 ± √(cosec²(pi/2)  1)
 1/tan(pi/2)
Note: Since pi/2 lies on the positive yaxis, the final value of cot pi/2 is 0.
We can use trigonometric identities to represent cot pi/2 as,
 tan (pi/2  pi/2) = tan 0
 tan (pi/2 + pi/2) = tan pi
 cot (pi  pi/2) = cot pi/2
☛ Also Check:
Examples Using Cot pi/2

Example 1: Using the value of cot pi/2, solve: (cosec²(pi/2)  1).
Solution:
We know, (cosec²(pi/2)  1) = (cot²(pi/2)) = 0
⇒ (cosec²(pi/2)  1) = 0 
Example 2: Find the value of 9 cot(pi/2)/10 cot(pi/4).
Solution:
Using trigonometric values, we know, cot(pi/2) = 0 and cot(pi/4) = 1.
⇒ Value of 9 cot(pi/2)/10 cot(pi/4) = 0 
Example 3: Simplify: 5 (cot(pi/2)/tan(pi/4))
Solution:
We know cot pi/2 = 0 and tan pi/4 = 1
⇒ 5 cot(pi/2)/tan(pi/4) = 0
FAQs on Cot pi/2
What is Cot pi/2?
Cot pi/2 is the value of cotangent trigonometric function for an angle equal to π/2 radians. The value of cot pi/2 is 0.
How to Find Cot pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot pi/2 can be given in terms of other trigonometric functions as:
 cos(pi/2)/sin(pi/2)
 ± cos(pi/2)/√(1  cos²(pi/2))
 ± √(1  sin²(pi/2))/sin(pi/2)
 ± 1/√(sec²(pi/2)  1)
 ± √(cosec²(pi/2)  1)
 1/tan(pi/2)
☛ Also check: trigonometry table
What is the Value of Cot pi/2 in Terms of Cos pi/2?
We know, using trig identities, we can write cot pi/2 as cos(pi/2)/√(1  cos²(pi/2)). Here, the value of cos pi/2 is equal to 0.
How to Find the Value of Cot pi/2?
The value of cot pi/2 can be calculated by constructing an angle of π/2 radians with the xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cot pi/2 is equal to the xcoordinate(0) divided by the ycoordinate (1). ∴ cot pi/2 = 0
What is the Value of Cot pi/2 in Terms of Cosec pi/2?
Since the cotangent function can be represented using the cosecant function, we can write cot pi/2 as √(cosec²(pi/2)  1). The value of cosec pi/2 is equal to 1.
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