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 x-axis.
• The cosec of pi/3 equals the reciprocal of the y-coordinate(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/√(1-cos²(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:

• sin pi/6
• sin 7pi
• sin 9pi/2
• tan 2pi/3
• sec pi/2
• cot pi/2

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/√(1-cos²(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 x-axis, 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 y-coordinate (0.866). ∴ csc pi/3 = 1.1547.