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 x-axis.
• The cosec of pi/6 equals the reciprocal of the y-coordinate(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/√(1-cos²(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:

• sin 4pi/3
• csc pi/3
• cos 11pi/6
• cos 5pi/4
• tan 2pi/3
• cos 15pi/4

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/√(1-cos²(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 x-axis, 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 y-coordinate (0.5). ∴ csc pi/6 = 2.