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 y-axis. 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 x-axis.
• The cot of 3pi/2 equals the x-coordinate(0) divided by y-coordinate(-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 y-axis, 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:

• cos 2pi/7
• cot pi/2
• cos 11pi/12
• sin 3pi/2
• sec pi/4
• sin pi/2

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 x-axis, 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 x-coordinate(0) divided by the y-coordinate (-1). ∴ cot 3pi/2 = 0