Cot 5pi/6

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

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

What is the Value of Cot 5pi/6?

The value of cot 5pi/6 in decimal is -1.732050807. . .. Cot 5pi/6 can also be expressed using the equivalent of the given angle (5pi/6) in degrees (150°).

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

Explanation:

For cot 5pi/6, the angle 5pi/6 lies between pi/2 and pi (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 5pi/6 value = -√3 or -1.7320508. . .
Since the cotangent function is a periodic function, we can represent cot 5pi/6 as, cot 5pi/6 = cot(5pi/6 + n × pi), n ∈ Z.
⇒ cot 5pi/6 = cot 11pi/6 = cot 17pi/6 , and so on.
Note: Since, cotangent is an odd function, the value of cot(-5pi/6) = -cot(5pi/6).

Methods to Find Value of Cot 5pi/6

The cotangent function is negative in the 2nd quadrant. The value of cot 5pi/6 is given as -1.73205. . .. We can find the value of cot 5pi/6 by:

• Using Trigonometric Functions
• Using Unit Circle

Cot 5pi/6 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 5pi/6 as:

• cos(5pi/6)/sin(5pi/6)
• ± cos(5pi/6)/√(1 - cos²(5pi/6))
• ± √(1 - sin²(5pi/6))/sin(5pi/6)
• ± 1/√(sec²(5pi/6) - 1)
• ± √(cosec²(5pi/6) - 1)
• 1/tan(5pi/6)

Note: Since 5pi/6 lies in the 2nd Quadrant, the final value of cot 5pi/6 will be negative.

We can use trigonometric identities to represent cot 5pi/6 as,

• tan (pi/2 - 5pi/6) = tan(-pi/3)
• -tan (pi/2 + 5pi/6) = -tan 4pi/3
• -cot (pi - 5pi/6) = -cot pi/6

Cot 5pi/6 Using Unit Circle

To find the value of cot 5π/6 using the unit circle:

• Rotate ‘r’ anticlockwise to form 5pi/6 angle with the positive x-axis.
• The cot of 5pi/6 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 5pi/6 = x/y = -1.7321 (approx)

☛ Also Check:

• sin 3pi
• cos pi/3
• sin pi/4
• sin 4pi/3
• tan 5pi/12
• tan 5pi/2

FAQs on Cot 5pi/6

What is Cot 5pi/6?

Cot 5pi/6 is the value of cotangent trigonometric function for an angle equal to 5π/6 radians. The value of cot 5pi/6 is -√3 or -1.7321 (approx).

How to Find Cot 5pi/6 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 5pi/6 can be given in terms of other trigonometric functions as:

• cos(5pi/6)/sin(5pi/6)
• ± cos(5pi/6)/√(1 - cos²(5pi/6))
• ± √(1 - sin²(5pi/6))/sin(5pi/6)
• ± 1/√(sec²(5pi/6) - 1)
• ± √(cosec²(5pi/6) - 1)
• 1/tan(5pi/6)

☛ Also check: trigonometric table

What is the Value of Cot 5pi/6 in Terms of Cosec 5pi/6?

Since the cotangent function can be represented using the cosecant function, we can write cot 5pi/6 as -√(cosec²(5pi/6) - 1). The value of cosec 5pi/6 is equal to 2.

How to Find the Value of Cot 5pi/6?

The value of cot 5pi/6 can be calculated by constructing an angle of 5π/6 radians 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 5pi/6 is equal to the x-coordinate(-0.866) divided by the y-coordinate (0.5). ∴ cot 5pi/6 = -1.7321

What is the Value of Cot 5pi/6 in Terms of Cos 5pi/6?

We know, using trig identities, we can write cot 5pi/6 as cos(5pi/6)/√(1 - cos²(5pi/6)). Here, the value of cos 5pi/6 is equal to -0.866025.