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 x-axis.
- The cot of 5pi/3 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 5pi/3 = x/y = -0.5774 (approx)
☛ Also Check:
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 x-axis, 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 x-coordinate(0.5) divided by the y-coordinate (-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.