from a handpicked tutor in LIVE 1to1 classes
Cot 5pi/3
The value of cot 5pi/3 is 0.5773502. . .. Cot 5pi/3 radians in degrees is written as cot ((5π/3) × 180°/π), i.e., cot (300°). In this article, we will discuss the methods to find the value of cot 5pi/3 with examples.
 Cot 5pi/3: (1/√3)
 Cot 5pi/3 in decimal: 0.5773502. . .
 Cot (5pi/3): 0.5773502. . . or 1/√3
 Cot 5pi/3 in degrees: cot (300°)
What is the Value of Cot 5pi/3?
The value of cot 5pi/3 in decimal is 0.577350269. . .. Cot 5pi/3 can also be expressed using the equivalent of the given angle (5pi/3) in degrees (300°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/3 radians = 5pi/3 × (180°/pi) = 300° or 300 degrees
∴ cot 5pi/3 = cot 5π/3 = cot(300°) = (1/√3) or 0.5773502. . .
Explanation:
For cot 5pi/3, the angle 5pi/3 lies between 3pi/2 and 2pi (Fourth Quadrant). Since cotangent function is negative in the fourth quadrant, thus cot 5pi/3 value = (1/√3) or 0.5773502. . .
Since the cotangent function is a periodic function, we can represent cot 5pi/3 as, cot 5pi/3 = cot(5pi/3 + n × pi), n ∈ Z.
⇒ cot 5pi/3 = cot 8pi/3 = cot 11pi/3 , and so on.
Note: Since, cotangent is an odd function, the value of cot(5pi/3) = cot(5pi/3).
Methods to Find Value of Cot 5pi/3
The cotangent function is negative in the 4th quadrant. The value of cot 5pi/3 is given as 0.57735. . .. We can find the value of cot 5pi/3 by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 5pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 5pi/3 as:
 cos(5pi/3)/sin(5pi/3)
 ± cos(5pi/3)/√(1  cos²(5pi/3))
 ± √(1  sin²(5pi/3))/sin(5pi/3)
 ± 1/√(sec²(5pi/3)  1)
 ± √(cosec²(5pi/3)  1)
 1/tan(5pi/3)
Note: Since 5pi/3 lies in the 4th Quadrant, the final value of cot 5pi/3 will be negative.
We can use trigonometric identities to represent cot 5pi/3 as,
 tan (pi/2  5pi/3) = tan(7pi/6)
 tan (pi/2 + 5pi/3) = tan 13pi/6
 cot (pi  5pi/3) = cot(2pi/3)
Cot 5pi/3 Using Unit Circle
To find the value of cot 5π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form 5pi/3 angle with the positive xaxis.
 The cot of 5pi/3 equals the xcoordinate(0.5) divided by ycoordinate(0.866) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of cot 5pi/3 = x/y = 0.5774 (approx)
☛ Also Check:
Examples Using Cot 5pi/3

Example 1: Find the value of 3 cot(5pi/3)/5 cot(2pi/3).
Solution:
Using trigonometric identities, we know, cot(5pi/3) = cot(pi  5pi/3) = cot(2pi/3).
⇒ cot(5pi/3) = cot(2pi/3)
⇒ Value of 3 cot(5pi/3)/5 cot(2pi/3) = 3/5 
Example 2: Simplify: 4 (cot(5pi/3)/tan(7pi/6))
Solution:
We know cot 5pi/3 = tan(7pi/6)
⇒ 4 cot(5pi/3)/tan(7pi/6) = 4 (cot(5pi/3)/cot(5pi/3))
= 4(1) = 4 
Example 3: Using the value of cot 5pi/3, solve: (cosec²(5pi/3)  1).
Solution:
We know, (cosec²(5pi/3)  1) = (cot²(5pi/3)) = 0.3333
⇒ (cosec²(5pi/3)  1) = 0.3333
FAQs on Cot 5pi/3
What is Cot 5pi/3?
Cot 5pi/3 is the value of cotangent trigonometric function for an angle equal to 5π/3 radians. The value of cot 5pi/3 is (1/√3) or 0.5774 (approx).
How to Find Cot 5pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 5pi/3 can be given in terms of other trigonometric functions as:
 cos(5pi/3)/sin(5pi/3)
 ± cos(5pi/3)/√(1  cos²(5pi/3))
 ± √(1  sin²(5pi/3))/sin(5pi/3)
 ± 1/√(sec²(5pi/3)  1)
 ± √(cosec²(5pi/3)  1)
 1/tan(5pi/3)
☛ Also check: trigonometry table
What is the Value of Cot 5pi/3 in Terms of Sin 5pi/3?
Using trigonometric identities, we can write cot 5pi/3 in terms of sin 5pi/3 as, cot(5pi/3) = √(1  sin²(5pi/3))/sin 5pi/3 . Here, the value of sin 5pi/3 is equal to (√3/2).
How to Find the Value of Cot 5pi/3?
The value of cot 5pi/3 can be calculated by constructing an angle of 5π/3 radians with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of cot 5pi/3 is equal to the xcoordinate(0.5) divided by the ycoordinate (0.866). ∴ cot 5pi/3 = 0.5774
What is the Value of Cot 5pi/3 in Terms of Cosec 5pi/3?
Since the cotangent function can be represented using the cosecant function, we can write cot 5pi/3 as √(cosec²(5pi/3)  1). The value of cosec 5pi/3 is equal to 1.15470.
visual curriculum