Cosec pi/6
The value of cosec pi/6 is 2. Cosec pi/6 radians in degrees is written as cosec ((π/6) × 180°/π), i.e., cosec (30°). In this article, we will discuss the methods to find the value of csc pi/6 with examples.
 Cosec pi/6: 2
 Cosec (pi/6): 2
 Cosec pi/6 in degrees: csc (30°)
What is the Value of Cosec pi/6?
The value of csc pi/6 is 2. Cosec pi/6 can also be expressed using the equivalent of the given angle (pi/6) in degrees (30°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/6 radians = pi/6 × (180°/pi) = 30° or 30 degrees
∴ csc pi/6 = csc π/6 = csc(30°) = 2
Explanation:
For csc pi/6, the angle pi/6 lies between 0 and pi/2 (First Quadrant). Since cosecant function is positive in the first quadrant, thus cosec pi/6 value = 2
Since the cosecant function is a periodic function, we can represent csc pi/6 as, cosec pi/6 = csc(pi/6 + n × 2pi), n ∈ Z.
⇒ csc pi/6 = csc 13pi/6 = cosec 25pi/6 , and so on.
Note: Since, cosecant is an odd function, the value of cosec(pi/6) = cosec(pi/6).
Methods to Find Value of Cosec pi/6
The cosecant function is positive in the 1st quadrant. The value of cosec pi/6 is given as 2. We can find the value of csc pi/6 by:
 Using Unit Circle
 Using Trigonometric Functions
Cosec pi/6 Using Unit Circle
To find the value of cosec π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/6 angle with the positive xaxis.
 The cosec of pi/6 equals the reciprocal of the ycoordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of cosec pi/6 = 1/y = 2
Cosec pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec pi/6 as:
 ± 1/√(1cos²(pi/6))
 ± √(1 + tan²(pi/6))/tan(pi/6)
 ± √(1 + cot²(pi/6))
 ± sec(pi/6)/√(sec²(pi/6)  1))
 1/sin(pi/6)
Note: Since pi/6 lies in the 1st Quadrant, the final value of csc pi/6 will be positive.
We can use trigonometric identities to represent csc pi/6 as,
 csc(pi  pi/6) = cosec 5pi/6
 cosec(pi + pi/6) = cosec 7pi/6
 sec(pi/2  pi/6) = sec pi/3
 sec(pi/2 + pi/6) = sec 2pi/3
☛ Also Check:
Examples Using Cosec pi/6

Example 1: Find the value of (sec(pi/12) csc(pi/12))/2. [Hint: Use csc pi/6 = 2]
Solution:
Using the sin 2a formula,
(sec(pi/12) csc(pi/12))/2 = 1/(2 × cos(pi/12) sin(pi/12)) = 1/sin(pi/6)
= 1/sin(pi/6) = csc pi/6 = 2
⇒ (sec(pi/12) csc(pi/12))/2 = 2 
Example 2: Simplify: 3 (csc(pi/6)/csc(13pi/6))
Solution:
We know csc pi/6 = csc 13pi/6
⇒ 3 csc(pi/6)/csc(13pi/6) = 3(csc(pi/6)/csc(pi/6))
= 3(1) = 3 
Example 3: Find the value of csc pi/6 if sin pi/6 is 0.5.
Solution:
Since, csc pi/6 = 1/sin(pi/6)
⇒ csc pi/6 = 1/0.5 = 2
FAQs on Cosec pi/6
What is Cosec pi/6?
Cosec pi/6 is the value of cosecant trigonometric function for an angle equal to π/6. The value of cosec pi/6 is 2.
How to Find Cosec pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of csc pi/6 can be given in terms of other trigonometric functions as:
 ± 1/√(1cos²(pi/6))
 ± √(1 + tan²(pi/6))/tan(pi/6)
 ± √(1 + cot²(pi/6))
 ± sec(pi/6)/√(sec²(pi/6)  1))
 1/sin(pi/6)
☛ Also check: trigonometry table
What is the Value of Cosec pi/6 in Terms of Sec pi/6?
Since the csc function can be represented using the secant function, we can write csc pi/6 as sec(pi/6)/√(sec²(pi/6)  1). The value of sec pi/6 is equal to 1.1547.
What is the Value of Csc pi/6 in Terms of Cos pi/6?
Using trigonometric identities, we can write csc pi/6 in terms of cos pi/6 as, csc(pi/6) = 1/√(1  cos²(pi/6)). Here, the value of cos pi/6 is equal to 0.866.
How to Find the Value of Cosec pi/6?
The value of csc pi/6 can be calculated by constructing an angle of π/6 radians with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of csc pi/6 is equal to the reciprocal of the ycoordinate (0.5). ∴ csc pi/6 = 2.
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