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Cot 240 Degrees

The value of cot 240 degrees is 0.5773502. . .. Cot 240 degrees in radians is written as cot (240° × π/180°), i.e., cot (4π/3) or cot (4.188790. . .). In this article, we will discuss the methods to find the value of cot 240 degrees with examples.

Cot 240°: 1/√3
Cot 240° in decimal: 0.5773502. . .
Cot (-240 degrees): -0.5773502. . . or -(1/√3)
Cot 240° in radians: cot (4π/3) or cot (4.1887902 . . .)

What is the Value of Cot 240 Degrees?

The value of cot 240 degrees in decimal is 0.577350269. . .. Cot 240 degrees can also be expressed using the equivalent of the given angle (240 degrees) in radians (4.18879 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 240 degrees = 240° × (π/180°) rad = 4π/3 or 4.1887 . . .
∴ cot 240° = cot(4.1887) = 1/√3 or 0.5773502. . .

Explanation:

For cot 240 degrees, the angle 240° lies between 180° and 270° (Third Quadrant). Since cotangent function is positive in the third quadrant, thus cot 240° value = 1/√3 or 0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot 240° as, cot 240 degrees = cot(240° + n × 180°), n ∈ Z.
⇒ cot 240° = cot 420° = cot 600°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-240°) = -cot(240°).

Methods to Find Value of Cot 240 Degrees

The cotangent function is positive in the 3rd quadrant. The value of cot 240° is given as 0.57735. . . We can find the value of cot 240 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cot 240° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 240 degrees as:

cos(240°)/sin(240°)
± cos 240°/√(1 - cos²(240°))
± √(1 - sin²(240°))/sin 240°
± 1/√(sec²(240°) - 1)
± √(cosec²(240°) - 1)
1/tan 240°

Note: Since 240° lies in the 3rd Quadrant, the final value of cot 240° will be positive.

We can use trigonometric identities to represent cot 240° as,

tan (90° - 240°) = tan(-150°)
-tan (90° + 240°) = -tan 330°
-cot (180° - 240°) = -cot(-60°)

Cot 240 Degrees Using Unit Circle

To find the value of cot 240 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 240° angle with the positive x-axis.
The cot of 240 degrees equals the x-coordinate(-0.5) divided by y-coordinate(-0.866) of the point of intersection (-0.5, -0.866) of unit circle and r.

Hence the value of cot 240° = x/y = 0.5774 (approx).

☛ Also Check:

Examples Using Cot 240 Degrees

Example 1: Using the value of cot 240°, solve: (cosec²(240°) - 1).

Solution:
We know, (cosec²(240°) - 1) = (cot²(240°)) = 0.3333
⇒ (cosec²(240°) - 1) = 0.3333
Example 2: Simplify: 8 (cot 240°/tan(-150°))

Solution:

We know cot 240° = tan(-150°)
⇒ 8 cot 240°/tan(-150°) = 8 (cot 240°/cot 240°)
= 8(1) = 8
Example 3: Find the value of (cos (240°) cosec (120°) sec (120°))/2. [Hint: Use cot 240° = 0.5774]

Solution:

Using trigonometry formulas,
(cos (240°) cosec (120°) sec (120°))/2 = cos (240°)/(2 sin (120°) cos (120°))
Using sin 2a formula,
2 sin (120°) cos (120°) = sin (2 × 120°) = sin 240°
⇒ cos (240°) / sin (240°) = cot 240°
⇒ (cos (240°) cosec (120°) sec (120°))/2 = 0.5774

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FAQs on Cot 240 Degrees

What is Cot 240 Degrees?

Cot 240 degrees is the value of cotangent trigonometric function for an angle equal to 240 degrees. The value of cot 240° is 1/√3 or 0.5774 (approx).

What is the Value of Cot 240° in Terms of Sec 240°?

We can represent the cotangent function in terms of the secant function using trig identities, cot 240° can be written as 1/√(sec²(240°) - 1). Here, the value of sec 240° is equal to -2.

How to Find Cot 240° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 240° can be given in terms of other trigonometric functions as:

cos(240°)/sin(240°)
± cos 240°/√(1 - cos²(240°))
± √(1 - sin²(240°))/sin 240°
± 1/√(sec²(240°) - 1)
± √(cosec²(240°) - 1)
1/tan 240°

☛ Also check: trigonometric table

What is the Value of Cot 240 Degrees in Terms of Cos 240°?

We know, using trig identities, we can write cot 240° as -cos 240°/√(1 - cos²(240°)). Here, the value of cos 240° is equal to -0.5.

How to Find the Value of Cot 240 Degrees?

The value of cot 240 degrees can be calculated by constructing an angle of 240° with the x-axis, and then finding the coordinates of the corresponding point (-0.5, -0.866) on the unit circle. The value of cot 240° is equal to the x-coordinate(-0.5) divided by the y-coordinate (-0.866). ∴ cot 240° = 0.5774

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