Cot 135 Degrees

The value of cot 135 degrees is -1. Cot 135 degrees in radians is written as cot (135° × π/180°), i.e., cot (3π/4) or cot (2.356194. . .). In this article, we will discuss the methods to find the value of cot 135 degrees with examples.

• Cot 135°: -1
• Cot (-135 degrees): 1
• Cot 135° in radians: cot (3π/4) or cot (2.3561944 . . .)

What is the Value of Cot 135 Degrees?

The value of cot 135 degrees is -1. Cot 135 degrees can also be expressed using the equivalent of the given angle (135 degrees) in radians (2.35619 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 135 degrees = 135° × (π/180°) rad = 3π/4 or 2.3561 . . .
∴ cot 135° = cot(2.3561) = -1

Explanation:

For cot 135 degrees, the angle 135° lies between 90° and 180° (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 135° value = -1
Since the cotangent function is a periodic function, we can represent cot 135° as, cot 135 degrees = cot(135° + n × 180°), n ∈ Z.
⇒ cot 135° = cot 315° = cot 495°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-135°) = -cot(135°).

Methods to Find Value of Cot 135 Degrees

The cotangent function is negative in the 2nd quadrant. The value of cot 135° is given as -1. We can find the value of cot 135 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 135 Degrees Using Unit Circle

To find the value of cot 135 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 135° angle with the positive x-axis.
• The cot of 135 degrees 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 135° = x/y = -1

Cot 135° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 135 degrees as:

• cos(135°)/sin(135°)
• ± cos 135°/√(1 - cos²(135°))
• ± √(1 - sin²(135°))/sin 135°
• ± 1/√(sec²(135°) - 1)
• ± √(cosec²(135°) - 1)
• 1/tan 135°

Note: Since 135° lies in the 2nd Quadrant, the final value of cot 135° will be negative.

We can use trigonometric identities to represent cot 135° as,

• tan (90° - 135°) = tan(-45°)
• -tan (90° + 135°) = -tan 225°
• -cot (180° - 135°) = -cot 45°

☛ Also Check:

• cot 45 degrees
• cot 210 degrees
• cot 10 degrees
• cot 7 degrees
• cot 105 degrees
• cot 238 degrees

FAQs on Cot 135 Degrees

What is Cot 135 Degrees?

Cot 135 degrees is the value of cotangent trigonometric function for an angle equal to 135 degrees. The value of cot 135° is -1.

What is the Value of Cot 135 Degrees in Terms of Sin 135°?

Using trigonometric identities, we can write cot 135° in terms of sin 135° as, cot(135°) = -√(1 - sin²(135°))/sin 135° . Here, the value of sin 135° is equal to 1/√2.

How to Find Cot 135° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 135° can be given in terms of other trigonometric functions as:

• cos(135°)/sin(135°)
• ± cos 135°/√(1 - cos²(135°))
• ± √(1 - sin²(135°))/sin 135°
• ± 1/√(sec²(135°) - 1)
• ± √(cosec²(135°) - 1)
• 1/tan 135°

☛ Also check: trigonometry table

How to Find the Value of Cot 135 Degrees?

The value of cot 135 degrees can be calculated by constructing an angle of 135° 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 135° is equal to the x-coordinate(-0.7071) divided by the y-coordinate (0.7071). ∴ cot 135° = -1

What is the Value of Cot 135° in Terms of Cosec 135°?

Since the cotangent function can be represented using the cosecant function, we can write cot 135° as -√(cosec²(135°) - 1). The value of cosec 135° is equal to 1.41421.