Cot 270 Degrees

The value of cot 270 degrees is 0. Cot 270 degrees in radians is written as cot (270° × π/180°), i.e., cot (3π/2) or cot (4.712388. . .). In this article, we will discuss the methods to find the value of cot 270 degrees with examples.

• Cot 270°: 0
• Cot (-270 degrees): 0
• Cot 270° in radians: cot (3π/2) or cot (4.7123889 . . .)

What is the Value of Cot 270 Degrees?

The value of cot 270 degrees is 0. Cot 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .
∴ cot 270° = cot(4.7123) = 0

Explanation:

For cot 270 degrees, the angle 270° lies on the negative y-axis. Thus cot 270° value = 0
Since the cotangent function is a periodic function, we can represent cot 270° as, cot 270 degrees = cot(270° + n × 180°), n ∈ Z.
⇒ cot 270° = cot 450° = cot 630°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-270°) = -cot(270°) = 0.

Methods to Find Value of Cot 270 Degrees

The value of cot 270° is given as 0. We can find the value of cot 270 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 270 Degrees Using Unit Circle

To find the value of cot 270 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 270° angle with the positive x-axis.
• The cot of 270 degrees equals the x-coordinate(0) divided by y-coordinate(-1) of the point of intersection (0, -1) of unit circle and r.

Hence the value of cot 270° = x/y = 0

Cot 270° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 270 degrees as:

• cos(270°)/sin(270°)
• ± cos 270°/√(1 - cos²(270°))
• ± √(1 - sin²(270°))/sin 270°
• ± 1/√(sec²(270°) - 1)
• ± √(cosec²(270°) - 1)
• 1/tan 270°

Note: Since 270° lies on the negative y-axis, the final value of cot 270° is 0.

We can use trigonometric identities to represent cot 270° as,

• tan (90° - 270°) = tan(-180°)
• -tan (90° + 270°) = -tan 360°
• -cot (180° - 270°) = -cot(-90°)

☛ Also Check:

• cot 132 degrees
• cot 18 degrees
• cot 25 degrees
• cot 135 degrees
• cot 37 degrees
• cot 105 degrees

FAQs on Cot 270 Degrees

What is Cot 270 Degrees?

Cot 270 degrees is the value of cotangent trigonometric function for an angle equal to 270 degrees. The value of cot 270° is 0.

How to Find the Value of Cot 270 Degrees?

The value of cot 270 degrees can be calculated by constructing an angle of 270° with the x-axis, and then finding the coordinates of the corresponding point (0, -1) on the unit circle. The value of cot 270° is equal to the x-coordinate(0) divided by the y-coordinate (-1). ∴ cot 270° = 0

What is the Value of Cot 270° in Terms of Sec 270°?

We can represent the cotangent function in terms of the secant function using trig identities, cot 270° can be written as 1/√(sec²(270°) - 1).

How to Find Cot 270° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 270° can be given in terms of other trigonometric functions as:

• cos(270°)/sin(270°)
• ± cos 270°/√(1 - cos²(270°))
• ± √(1 - sin²(270°))/sin 270°
• ± 1/√(sec²(270°) - 1)
• ± √(cosec²(270°) - 1)
• 1/tan 270°

☛ Also check: trigonometry table

What is the Value of Cot 270 Degrees in Terms of Sin 270°?

Using trigonometric identities, we can write cot 270° in terms of sin 270° as, cot(270°) = -√(1 - sin²(270°))/sin 270°. Here, the value of sin 270° is equal to -1.