Cot 3pi/4

The value of cot 3pi/4 is -1. Cot 3pi/4 radians in degrees is written as cot ((3π/4) × 180°/π), i.e., cot (135°). In this article, we will discuss the methods to find the value of cot 3pi/4 with examples.

• Cot 3pi/4: -1
• Cot (-3pi/4): 1
• Cot 3pi/4 in degrees: cot (135°)

What is the Value of Cot 3pi/4?

The value of cot 3pi/4 is -1. Cot 3pi/4 can also be expressed using the equivalent of the given angle (3pi/4) in degrees (135°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 3pi/4 radians = 3pi/4 × (180°/pi) = 135° or 135 degrees
∴ cot 3pi/4 = cot 3π/4 = cot(135°) = -1

Explanation:

For cot 3pi/4, the angle 3pi/4 lies between pi/2 and pi (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 3pi/4 value = -1
Since the cotangent function is a periodic function, we can represent cot 3pi/4 as, cot 3pi/4 = cot(3pi/4 + n × pi), n ∈ Z.
⇒ cot 3pi/4 = cot 7pi/4 = cot 11pi/4 , and so on.
Note: Since, cotangent is an odd function, the value of cot(-3pi/4) = -cot(3pi/4).

Methods to Find Value of Cot 3pi/4

The cotangent function is negative in the 2nd quadrant. The value of cot 3pi/4 is given as -1. We can find the value of cot 3pi/4 by:

• Using Trigonometric Functions
• Using Unit Circle

Cot 3pi/4 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 3pi/4 as:

• cos(3pi/4)/sin(3pi/4)
• ± cos(3pi/4)/√(1 - cos²(3pi/4))
• ± √(1 - sin²(3pi/4))/sin(3pi/4)
• ± 1/√(sec²(3pi/4) - 1)
• ± √(cosec²(3pi/4) - 1)
• 1/tan(3pi/4)

Note: Since 3pi/4 lies in the 2nd Quadrant, the final value of cot 3pi/4 will be negative.

We can use trigonometric identities to represent cot 3pi/4 as,

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

Cot 3pi/4 Using Unit Circle

To find the value of cot 3π/4 using the unit circle:

• Rotate ‘r’ anticlockwise to form 3pi/4 angle with the positive x-axis.
• The cot of 3pi/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 3pi/4 = x/y = -1

☛ Also Check:

• cos 3pi
• sin 11pi/6
• tan 11pi 6
• sin 5pi/6
• tan 3pi/8
• cos 7pi/6

FAQs on Cot 3pi/4

What is Cot 3pi/4?

Cot 3pi/4 is the value of cotangent trigonometric function for an angle equal to 3π/4 radians. The value of cot 3pi/4 is -1.

What is the Value of Cot 3pi/4 in Terms of Cosec 3pi/4?

Since the cotangent function can be represented using the cosecant function, we can write cot 3pi/4 as -√(cosec²(3pi/4) - 1). The value of cosec 3pi/4 is equal to 1.41421.

What is the Value of Cot 3pi/4 in Terms of Cos 3pi/4?

We know, using trig identities, we can write cot 3pi/4 as cos(3pi/4)/√(1 - cos²(3pi/4)). Here, the value of cos 3pi/4 is equal to -0.707106.

How to Find the Value of Cot 3pi/4?

The value of cot 3pi/4 can be calculated by constructing an angle of 3π/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 3pi/4 is equal to the x-coordinate(-0.7071) divided by the y-coordinate (0.7071). ∴ cot 3pi/4 = -1

How to Find Cot 3pi/4 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 3pi/4 can be given in terms of other trigonometric functions as:

• cos(3pi/4)/sin(3pi/4)
• ± cos(3pi/4)/√(1 - cos²(3pi/4))
• ± √(1 - sin²(3pi/4))/sin(3pi/4)
• ± 1/√(sec²(3pi/4) - 1)
• ± √(cosec²(3pi/4) - 1)
• 1/tan(3pi/4)

☛ Also check: trigonometry table