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Cosec pi/3
The value of cosec pi/3 is 1.1547005. . .. Cosec pi/3 radians in degrees is written as csc ((π/3) × 180°/π), i.e., csc (60°). In this article, we will discuss the methods to find the value of cosec pi/3 with examples.
 Cosec pi/3: 2/√3
 Cosec pi/3 in decimal: 1.1547005. . .
 Cosec (pi/3): 1.1547005. . . or 2/√3
 Cosec pi/3 in degrees: csc (60°)
What is the Value of Cosec pi/3?
The value of cosec pi/3 in decimal is 1.154700538. . .. Cosec pi/3 can also be expressed using the equivalent of the given angle (pi/3) in degrees (60°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/3 radians = pi/3 × (180°/pi) = 60° or 60 degrees
∴ cosec pi/3 = cosec π/3 = cosec(60°) = 2/√3 or 1.1547005. . .
Explanation:
For cosec pi/3, the angle pi/3 lies between 0 and pi/2 (First Quadrant). Since cosecant function is positive in the first quadrant, thus cosec pi/3 value = 2/√3 or 1.1547005. . .
Since the cosecant function is a periodic function, we can represent cosec pi/3 as, csc pi/3 = csc(pi/3 + n × 2pi), n ∈ Z.
⇒ cosec pi/3 = cosec 7pi/3 = csc 13pi/3 , and so on.
Note: Since, cosecant is an odd function, the value of csc(pi/3) = cosec(pi/3).
Methods to Find Value of Cosec pi/3
The cosecant function is positive in the 1st quadrant. The value of csc pi/3 is given as 1.15470. . .. We can find the value of csc pi/3 by:
 Using Unit Circle
 Using Trigonometric Functions
Cosec pi/3 Using Unit Circle
To find the value of cosec π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/3 angle with the positive xaxis.
 The cosec of pi/3 equals the reciprocal of the ycoordinate(0.866) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of cosec pi/3 = 1/y = 1.1547 (approx)
Cosec pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the csc pi/3 as:
 ± 1/√(1cos²(pi/3))
 ± √(1 + tan²(pi/3))/tan(pi/3)
 ± √(1 + cot²(pi/3))
 ± sec(pi/3)/√(sec²(pi/3)  1))
 1/sin(pi/3)
Note: Since pi/3 lies in the 1st Quadrant, the final value of cosec pi/3 will be positive.
We can use trigonometric identities to represent cosec pi/3 as,
 cosec(pi  pi/3) = csc 2pi/3
 cosec(pi + pi/3) = cosec 4pi/3
 sec(pi/2  pi/3) = sec pi/6
 sec(pi/2 + pi/3) = sec 5pi/6
☛ Also Check:
Examples Using Cosec pi/3

Example 1: Find the value of 5 cosec(pi/3)/9 sec(pi/6).
Solution:
Using trigonometric identities, we know, csc(pi/3) = sec(pi/2  pi/3) = sec pi/6.
⇒ csc(pi/3) = sec(pi/6)
⇒ Value of 5 cosec(pi/3)/9 sec(pi/6) = 5/9 
Example 2: Find the value of csc pi/3 if sin pi/3 is 0.8660.
Solution:
Since, csc pi/3 = 1/sin(pi/3)
⇒ csc pi/3 = 1/0.8660 = 1.1547 
Example 3: Simplify: 10 (csc(pi/3)/csc(7pi/3))
Solution:
We know csc pi/3 = csc 7pi/3
⇒ 10 csc(pi/3)/csc(7pi/3) = 10(csc(pi/3)/csc(pi/3))
= 10(1) = 10
FAQs on Cosec pi/3
What is Cosec pi/3?
Cosec pi/3 is the value of cosecant trigonometric function for an angle equal to π/3. The value of cosec pi/3 is 2/√3 or 1.1547 (approx).
How to Find Cosec pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of csc pi/3 can be given in terms of other trigonometric functions as:
 ± 1/√(1cos²(pi/3))
 ± √(1 + tan²(pi/3))/tan(pi/3)
 ± √(1 + cot²(pi/3))
 ± sec(pi/3)/√(sec²(pi/3)  1))
 1/sin(pi/3)
☛ Also check: trigonometric table
What is the Value of Csc pi/3 in Terms of Cos pi/3?
Using trigonometric identities, we can write csc pi/3 in terms of cos pi/3 as, csc(pi/3) = 1/√(1  cos²(pi/3)). Here, the value of cos pi/3 is equal to 0.5.
What is the Exact Value of Cosec pi/3?
The exact value of cosec pi/3 can be given accurately up to 8 decimal places as 1.15470053 or as 2/√3.
How to Find the Value of Cosec pi/3?
The value of csc pi/3 can be calculated by constructing an angle of π/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 csc pi/3 is equal to the reciprocal of the ycoordinate (0.866). ∴ csc pi/3 = 1.1547.
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