Cosec 60 Degrees
The value of cosec 60 degrees is 1.1547005. . .. Cosec 60 degrees in radians is written as cosec (60° × π/180°), i.e., cosec (π/3) or cosec (1.047197. . .). In this article, we will discuss the methods to find the value of cosec 60 degrees with examples.
 Cosec 60°: 2/√3
 Cosec 60° in decimal: 1.1547005. . .
 Cosec (60 degrees): 1.1547005. . . or 2/√3
 Cosec 60° in radians: cosec (π/3) or cosec (1.0471975 . . .)
What is the Value of Cosec 60 Degrees?
The value of cosec 60 degrees in decimal is 1.154700538. . .. Cosec 60 degrees can also be expressed using the equivalent of the given angle (60 degrees) in radians (1.04719 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 60 degrees = 60° × (π/180°) rad = π/3 or 1.0471 . . .
∴ cosec 60° = cosec(1.0471) = 2/√3 or 1.1547005. . .
Explanation:
For cosec 60 degrees, the angle 60° lies between 0° and 90° (First Quadrant). Since cosecant function is positive in the first quadrant, thus cosec 60° value = 2/√3 or 1.1547005. . .
Since the cosecant function is a periodic function, we can represent cosec 60° as, cosec 60 degrees = cosec(60° + n × 360°), n ∈ Z.
⇒ cosec 60° = cosec 420° = cosec 780°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(60°) = cosec(60°).
Methods to Find Value of Cosec 60 Degrees
The cosecant function is positive in the 1st quadrant. The value of cosec 60° is given as 1.15470. . .. We can find the value of cosec 60 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cosec 60° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec 60 degrees as:
 ± 1/√(1cos²(60°))
 ± √(1 + tan²(60°))/tan 60°
 ± √(1 + cot²(60°))
 ± sec 60°/√(sec²(60°)  1)
 1/sin 60°
Note: Since 60° lies in the 1st Quadrant, the final value of cosec 60° will be positive.
We can use trigonometric identities to represent cosec 60° as,
 cosec(180°  60°) = cosec 120°
 cosec(180° + 60°) = cosec 240°
 sec(90°  60°) = sec 30°
 sec(90° + 60°) = sec 150°
Cosec 60 Degrees Using Unit Circle
To find the value of cosec 60 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 60° angle with the positive xaxis.
 The cosec of 60 degrees 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 60° = 1/y = 1.1547 (approx)
☛ Also Check:
Examples Using Cosec 60 Degrees

Example 1: Using the value of csc 60°, solve: (1 + cot²(60°)).
Solution:
We know, (1 + cot²(60°)) = (csc²(60°)) = 1.3333
⇒ (1 + cot²(60°)) = 1.3333 
Example 2: Find the value of csc 60° if sin 60° is 0.8660.
Solution:
Since, csc 60° = 1/sin 60°
⇒ csc 60° = 1/0.8660 = 1.1547 
Example 3: Find the value of (sec 30° cosec 30°)/2. [Hint: Use cosec 60° = 1.1547]
Solution:
Using the sin 2a formula,
(sec 30° cosec 30°)/2 = 1/(2 × cos 30° sin 30°) = 1/sin 60°
= 1/sin 60° = cosec 60° = 1.1547
⇒ (sec 30° cosec 30°)/2 = 1.1547
FAQs on Cosec 60 Degrees
What is Cosec 60 Degrees?
Cosec 60 degrees is the value of cosecant trigonometric function for an angle equal to 60 degrees. The value of cosec 60° is 2/√3 or 1.1547 (approx).
How to Find the Value of Cosec 60 Degrees?
The value of cosec 60 degrees can be calculated by constructing an angle of 60° with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of cosec 60° is equal to the reciprocal of the ycoordinate (0.866). ∴ cosec 60° = 1.1547.
What is the Value of Cosec 60 Degrees in Terms of Cot 60°?
We can represent the cosec function in terms of the cotangent function using trig identities, cosec 60° can be written as √(1 + cot²(60°)). Here, the value of cot 60° is equal to 0.5774.
What is the Value of Cosec 60° in Terms of Sec 60°?
Since the cosec function can be represented using the secant function, we can write cosec 60° as sec 60°/√(sec²(60°)  1). The value of sec 60° is equal to 2.
How to Find Cosec 60° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cosec 60° can be given in terms of other trigonometric functions as:
 ± 1/√(1cos²(60°))
 ± √(1 + tan²(60°))/tan 60°
 ± √(1 + cot²(60°))
 ± sec 60°/√(sec²(60°)  1)
 1/sin 60°
☛ Also check: trigonometry table
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