Cot 5pi/4

The value of cot 5pi/4 is 1. Cot 5pi/4 radians in degrees is written as cot ((5π/4) × 180°/π), i.e., cot (225°). In this article, we will discuss the methods to find the value of cot 5pi/4 with examples.

• Cot 5pi/4: 1
• Cot (-5pi/4): -1
• Cot 5pi/4 in degrees: cot (225°)

What is the Value of Cot 5pi/4?

The value of cot 5pi/4 is 1. Cot 5pi/4 can also be expressed using the equivalent of the given angle (5pi/4) in degrees (225°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/4 radians = 5pi/4 × (180°/pi) = 225° or 225 degrees
∴ cot 5pi/4 = cot 5π/4 = cot(225°) = 1

Explanation:

For cot 5pi/4, the angle 5pi/4 lies between pi and 3pi/2 (Third Quadrant). Since cotangent function is positive in the third quadrant, thus cot 5pi/4 value = 1
Since the cotangent function is a periodic function, we can represent cot 5pi/4 as, cot 5pi/4 = cot(5pi/4 + n × pi), n ∈ Z.
⇒ cot 5pi/4 = cot 9pi/4 = cot 13pi/4 , and so on.
Note: Since, cotangent is an odd function, the value of cot(-5pi/4) = -cot(5pi/4).

Methods to Find Value of Cot 5pi/4

The cotangent function is positive in the 3rd quadrant. The value of cot 5pi/4 is given as 1. We can find the value of cot 5pi/4 by:

• Using Trigonometric Functions
• Using Unit Circle

Cot 5pi/4 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 5pi/4 as:

• cos(5pi/4)/sin(5pi/4)
• ± cos(5pi/4)/√(1 - cos²(5pi/4))
• ± √(1 - sin²(5pi/4))/sin(5pi/4)
• ± 1/√(sec²(5pi/4) - 1)
• ± √(cosec²(5pi/4) - 1)
• 1/tan(5pi/4)

Note: Since 5pi/4 lies in the 3rd Quadrant, the final value of cot 5pi/4 will be positive.

We can use trigonometric identities to represent cot 5pi/4 as,

• tan (pi/2 - 5pi/4) = tan(-3pi/4)
• -tan (pi/2 + 5pi/4) = -tan 7pi/4
• -cot (pi - 5pi/4) = -cot(-pi/4)

Cot 5pi/4 Using Unit Circle

To find the value of cot 5π/4 using the unit circle:

• Rotate ‘r’ anticlockwise to form 5pi/4 angle with the positive x-axis.
• The cot of 5pi/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 5pi/4 = x/y = 1

☛ Also Check:

• sin 5pi/4
• sin pi/6
• cos pi
• cos 7pi/4
• tan 7pi/6
• cos 13pi/6

FAQs on Cot 5pi/4

What is Cot 5pi/4?

Cot 5pi/4 is the value of cotangent trigonometric function for an angle equal to 5π/4 radians. The value of cot 5pi/4 is 1.

What is the Value of Cot 5pi/4 in Terms of Sec 5pi/4?

We can represent the cotangent function in terms of the secant function using trig identities, cot 5pi/4 can be written as 1/√(sec²(5pi/4) - 1). Here, the value of sec 5pi/4 is equal to -1.4142.

How to Find Cot 5pi/4 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 5pi/4 can be given in terms of other trigonometric functions as:

• cos(5pi/4)/sin(5pi/4)
• ± cos(5pi/4)/√(1 - cos²(5pi/4))
• ± √(1 - sin²(5pi/4))/sin(5pi/4)
• ± 1/√(sec²(5pi/4) - 1)
• ± √(cosec²(5pi/4) - 1)
• 1/tan(5pi/4)

☛ Also check: trigonometric table

How to Find the Value of Cot 5pi/4?

The value of cot 5pi/4 can be calculated by constructing an angle of 5π/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 5pi/4 is equal to the x-coordinate(-0.7071) divided by the y-coordinate (-0.7071). ∴ cot 5pi/4 = 1

What is the Value of Cot 5pi/4 in Terms of Cos 5pi/4?

We know, using trig identities, we can write cot 5pi/4 as -cos(5pi/4)/√(1 - cos²(5pi/4)). Here, the value of cos 5pi/4 is equal to -0.707106.