Cot 150 Degrees

The value of cot 150 degrees is -1.7320508. . .. Cot 150 degrees in radians is written as cot (150° × π/180°), i.e., cot (5π/6) or cot (2.617993. . .). In this article, we will discuss the methods to find the value of cot 150 degrees with examples.

• Cot 150°: -√3
• Cot 150° in decimal: -1.7320508. . .
• Cot (-150 degrees): 1.7320508. . . or √3
• Cot 150° in radians: cot (5π/6) or cot (2.6179938 . . .)

What is the Value of Cot 150 Degrees?

The value of cot 150 degrees in decimal is -1.732050807. . .. Cot 150 degrees can also be expressed using the equivalent of the given angle (150 degrees) in radians (2.61799 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 150 degrees = 150° × (π/180°) rad = 5π/6 or 2.6179 . . .
∴ cot 150° = cot(2.6179) = -√3 or -1.7320508. . .

Explanation:

For cot 150 degrees, the angle 150° lies between 90° and 180° (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 150° value = -√3 or -1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot 150° as, cot 150 degrees = cot(150° + n × 180°), n ∈ Z.
⇒ cot 150° = cot 330° = cot 510°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-150°) = -cot(150°).

Methods to Find Value of Cot 150 Degrees

The cotangent function is negative in the 2nd quadrant. The value of cot 150° is given as -1.73205. . . We can find the value of cot 150 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 150 Degrees Using Unit Circle

To find the value of cot 150 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 150° angle with the positive x-axis.
• The cot of 150 degrees equals the x-coordinate(-0.866) divided by y-coordinate(0.5) of the point of intersection (-0.866, 0.5) of unit circle and r.

Hence the value of cot 150° = x/y = -1.7321 (approx).

Cot 150° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 150 degrees as:

• cos(150°)/sin(150°)
• ± cos 150°/√(1 - cos²(150°))
• ± √(1 - sin²(150°))/sin 150°
• ± 1/√(sec²(150°) - 1)
• ± √(cosec²(150°) - 1)
• 1/tan 150°

Note: Since 150° lies in the 2nd Quadrant, the final value of cot 150° will be negative.

We can use trigonometric identities to represent cot 150° as,

• tan (90° - 150°) = tan(-60°)
• -tan (90° + 150°) = -tan 240°
• -cot (180° - 150°) = -cot 30°

☛ Also Check:

• cot 4 degrees
• cot 765 degrees
• cot 270 degrees
• cot 238 degrees
• cot 12 degrees
• cot 34 degrees

FAQs on Cot 150 Degrees

What is Cot 150 Degrees?

Cot 150 degrees is the value of cotangent trigonometric function for an angle equal to 150 degrees. The value of cot 150° is -√3 or -1.7321 (approx).

What is the Exact Value of Cot 150 Degrees?

The exact value of cot 150 degrees can be given accurately up to 8 decimal places as -1.73205080 or as -√3.

How to Find Cot 150° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 150° can be given in terms of other trigonometric functions as:

• cos(150°)/sin(150°)
• ± cos 150°/√(1 - cos²(150°))
• ± √(1 - sin²(150°))/sin 150°
• ± 1/√(sec²(150°) - 1)
• ± √(cosec²(150°) - 1)
• 1/tan 150°

☛ Also check: trigonometric table

What is the Value of Cot 150 Degrees in Terms of Sin 150°?

Using trigonometric identities, we can write cot 150° in terms of sin 150° as, cot(150°) = -√(1 - sin²(150°))/sin 150° . Here, the value of sin 150° is equal to 1/2.

How to Find the Value of Cot 150 Degrees?

The value of cot 150 degrees can be calculated by constructing an angle of 150° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, 0.5) on the unit circle. The value of cot 150° is equal to the x-coordinate(-0.866) divided by the y-coordinate (0.5). ∴ cot 150° = -1.7321