Cot 225 Degrees

The value of cot 225 degrees is 1. Cot 225 degrees in radians is written as cot (225° × π/180°), i.e., cot (5π/4) or cot (3.926990. . .). In this article, we will discuss the methods to find the value of cot 225 degrees with examples.

• Cot 225°: 1
• Cot (-225 degrees): -1
• Cot 225° in radians: cot (5π/4) or cot (3.9269908 . . .)

What is the Value of Cot 225 Degrees?

The value of cot 225 degrees is 1. Cot 225 degrees can also be expressed using the equivalent of the given angle (225 degrees) in radians (3.92699 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 225 degrees = 225° × (π/180°) rad = 5π/4 or 3.9269 . . .
∴ cot 225° = cot(3.9269) = 1

Explanation:

For cot 225 degrees, the angle 225° lies between 180° and 270° (Third Quadrant). Since cotangent function is positive in the third quadrant, thus cot 225° value = 1
Since the cotangent function is a periodic function, we can represent cot 225° as, cot 225 degrees = cot(225° + n × 180°), n ∈ Z.
⇒ cot 225° = cot 405° = cot 585°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-225°) = -cot(225°).

Methods to Find Value of Cot 225 Degrees

The cotangent function is positive in the 3rd quadrant. The value of cot 225° is given as 1. We can find the value of cot 225 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 225 Degrees Using Unit Circle

To find the value of cot 225 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 225° angle with the positive x-axis.
• The cot of 225 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 225° = x/y = 1

Cot 225° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 225 degrees as:

• cos(225°)/sin(225°)
• ± cos 225°/√(1 - cos²(225°))
• ± √(1 - sin²(225°))/sin 225°
• ± 1/√(sec²(225°) - 1)
• ± √(cosec²(225°) - 1)
• 1/tan 225°

Note: Since 225° lies in the 3rd Quadrant, the final value of cot 225° will be positive.

We can use trigonometric identities to represent cot 225° as,

• tan (90° - 225°) = tan(-135°)
• -tan (90° + 225°) = -tan 315°
• -cot (180° - 225°) = -cot(-45°)

☛ Also Check:

• cot 34 degrees
• cot 70 degrees
• cot 120 degrees
• cot 11 degrees
• cot 50 degrees
• cot 40 degrees

FAQs on Cot 225 Degrees

What is Cot 225 Degrees?

Cot 225 degrees is the value of cotangent trigonometric function for an angle equal to 225 degrees. The value of cot 225° is 1.

What is the Value of Cot 225 Degrees in Terms of Sin 225°?

Using trigonometric identities, we can write cot 225° in terms of sin 225° as, cot(225°) = -√(1 - sin²(225°))/sin 225° . Here, the value of sin 225° is equal to -(1/√2).

How to Find the Value of Cot 225 Degrees?

The value of cot 225 degrees can be calculated by constructing an angle of 225° 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 225° is equal to the x-coordinate(-0.7071) divided by the y-coordinate (-0.7071). ∴ cot 225° = 1

How to Find Cot 225° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 225° can be given in terms of other trigonometric functions as:

• cos(225°)/sin(225°)
• ± cos 225°/√(1 - cos²(225°))
• ± √(1 - sin²(225°))/sin 225°
• ± 1/√(sec²(225°) - 1)
• ± √(cosec²(225°) - 1)
• 1/tan 225°

☛ Also check: trigonometry table

What is the Exact Value of Cot 225 Degrees?

The exact value of cot 225 degrees is 1.