Cot pi/4

The value of cot pi/4 is 1. Cot pi/4 radians in degrees is written as cot ((π/4) × 180°/π), i.e., cot (45°). In this article, we will discuss the methods to find the value of cot pi/4 with examples.

• Cot pi/4: 1
• Cot (-pi/4): -1
• Cot pi/4 in degrees: cot (45°)

What is the Value of Cot pi/4?

The value of cot pi/4 is 1. Cot pi/4 can also be expressed using the equivalent of the given angle (pi/4) in degrees (45°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/4 radians = pi/4 × (180°/pi) = 45° or 45 degrees
∴ cot pi/4 = cot π/4 = cot(45°) = 1

Explanation:

For cot pi/4, the angle pi/4 lies between 0 and pi/2 (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot pi/4 value = 1
Since the cotangent function is a periodic function, we can represent cot pi/4 as, cot pi/4 = cot(pi/4 + n × pi), n ∈ Z.
⇒ cot pi/4 = cot 5pi/4 = cot 9pi/4 , and so on.
Note: Since, cotangent is an odd function, the value of cot(-pi/4) = -cot(pi/4).

Methods to Find Value of Cot pi/4

The cotangent function is positive in the 1st quadrant. The value of cot pi/4 is given as 1. We can find the value of cot pi/4 by:

• Using Trigonometric Functions
• Using Unit Circle

Cot pi/4 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot pi/4 as:

• cos(pi/4)/sin(pi/4)
• ± cos(pi/4)/√(1 - cos²(pi/4))
• ± √(1 - sin²(pi/4))/sin(pi/4)
• ± 1/√(sec²(pi/4) - 1)
• ± √(cosec²(pi/4) - 1)
• 1/tan(pi/4)

Note: Since pi/4 lies in the 1st Quadrant, the final value of cot pi/4 will be positive.

We can use trigonometric identities to represent cot pi/4 as,

• tan (pi/2 - pi/4) = tan pi/4
• -tan (pi/2 + pi/4) = -tan 3pi/4
• -cot (pi - pi/4) = -cot 3pi/4

Cot pi/4 Using Unit Circle

To find the value of cot π/4 using the unit circle:

• Rotate ‘r’ anticlockwise to form pi/4 angle with the positive x-axis.
• The cot of pi/4 equals the x-coordinate(0.7071) divided by y-coordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.

Hence the value of cot pi/4 = x/y = 1

☛ Also Check:

• cot 2pi
• tan pi/2
• cos 4pi
• tan 7pi/4
• tan pi/4
• tan 2pi

FAQs on Cot pi/4

What is Cot pi/4?

Cot pi/4 is the value of cotangent trigonometric function for an angle equal to π/4 radians. The value of cot pi/4 is 1.

How to Find the Value of Cot pi/4?

The value of cot pi/4 can be calculated by constructing an angle of π/4 radians with the x-axis, and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of cot pi/4 is equal to the x-coordinate(0.7071) divided by the y-coordinate (0.7071). ∴ cot pi/4 = 1

How to Find Cot pi/4 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot pi/4 can be given in terms of other trigonometric functions as:

• cos(pi/4)/sin(pi/4)
• ± cos(pi/4)/√(1 - cos²(pi/4))
• ± √(1 - sin²(pi/4))/sin(pi/4)
• ± 1/√(sec²(pi/4) - 1)
• ± √(cosec²(pi/4) - 1)
• 1/tan(pi/4)

☛ Also check: trigonometric table

What is the Value of Cot pi/4 in Terms of Tan pi/4?

Since the cotangent function is the reciprocal of the tangent function, we can write cot pi/4 as 1/tan(pi/4). The value of tan pi/4 is equal to 1.

What is the Exact Value of Cot pi/4?

The exact value of cot pi/4 is 1.