Cosec 2 Degrees
The value of cosec 2 degrees is 28.6537083. . .. Cosec 2 degrees in radians is written as cosec (2° × π/180°), i.e., cosec (π/90) or cosec (0.034906. . .). In this article, we will discuss the methods to find the value of cosec 2 degrees with examples.
 Cosec 2° in decimal: 28.6537083. . .
 Cosec (2 degrees): 28.6537083. . .
 Cosec 2° in radians: cosec (π/90) or cosec (0.0349065 . . .)
What is the Value of Cosec 2 Degrees?
The value of cosec 2 degrees in decimal is 28.653708347. . .. Cosec 2 degrees can also be expressed using the equivalent of the given angle (2 degrees) in radians (0.03490 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 2 degrees = 2° × (π/180°) rad = π/90 or 0.0349 . . .
∴ cosec 2° = cosec(0.0349) = 28.6537083. . .
Explanation:
For cosec 2 degrees, the angle 2° lies between 0° and 90° (First Quadrant). Since cosecant function is positive in the first quadrant, thus cosec 2° value = 28.6537083. . .
Since the cosecant function is a periodic function, we can represent cosec 2° as, cosec 2 degrees = cosec(2° + n × 360°), n ∈ Z.
⇒ cosec 2° = cosec 362° = cosec 722°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(2°) = cosec(2°).
Methods to Find Value of Cosec 2 Degrees
The cosecant function is positive in the 1st quadrant. The value of cosec 2° is given as 28.65370. . .. We can find the value of cosec 2 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cosec 2° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec 2 degrees as:
 ± 1/√(1cos²(2°))
 ± √(1 + tan²(2°))/tan 2°
 ± √(1 + cot²(2°))
 ± sec 2°/√(sec²(2°)  1)
 1/sin 2°
Note: Since 2° lies in the 1st Quadrant, the final value of cosec 2° will be positive.
We can use trigonometric identities to represent cosec 2° as,
 cosec(180°  2°) = cosec 178°
 cosec(180° + 2°) = cosec 182°
 sec(90°  2°) = sec 88°
 sec(90° + 2°) = sec 92°
Cosec 2 Degrees Using Unit Circle
To find the value of cosec 2 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 2° angle with the positive xaxis.
 The cosec of 2 degrees equals the reciprocal of the ycoordinate(0.0349) of the point of intersection (0.9994, 0.0349) of unit circle and r.
Hence the value of cosec 2° = 1/y = 28.6537 (approx)
☛ Also Check:
Examples Using Cosec 2 Degrees

Example 1: Using the value of csc 2°, solve: (1 + cot²(2°)).
Solution:
We know, (1 + cot²(2°)) = (csc²(2°)) = 821.035
⇒ (1 + cot²(2°)) = 821.035 
Example 2: Find the value of (sec 1° cosec 1°)/2. [Hint: Use cosec 2° = 28.6537]
Solution:
Using the sin 2a formula,
(sec 1° cosec 1°)/2 = 1/(2 × cos 1° sin 1°) = 1/sin 2°
= 1/sin 2° = cosec 2° = 28.6537
⇒ (sec 1° cosec 1°)/2 = 28.6537 
Example 3: Simplify: 12 (cosec 2°/cosec 362°)
Solution:
We know cosec 2° = cosec 362°
⇒ 12 cosec 2°/cosec 362° = 12(cosec 2°/cosec 2°)
= 12(1) = 12
FAQs on Cosec 2 Degrees
What is Cosec 2 Degrees?
Cosec 2 degrees is the value of cosecant trigonometric function for an angle equal to 2 degrees. The value of cosec 2° is 28.6537 (approx).
What is the Value of Csc 2° in Terms of Sin 2°?
Since the cosecant function is the reciprocal of the sine function, we can write csc 2° as 1/sin(2°). The value of sin 2° is equal to 0.0349.
What is the Value of Cosec 2 Degrees in Terms of Cot 2°?
We can represent the cosec function in terms of the cotangent function using trig identities, cosec 2° can be written as √(1 + cot²(2°)). Here, the value of cot 2° is equal to 28.6363.
How to Find Cosec 2° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cosec 2° can be given in terms of other trigonometric functions as:
 ± 1/√(1cos²(2°))
 ± √(1 + tan²(2°))/tan 2°
 ± √(1 + cot²(2°))
 ± sec 2°/√(sec²(2°)  1)
 1/sin 2°
☛ Also check: trigonometric table
How to Find the Value of Cosec 2 Degrees?
The value of cosec 2 degrees can be calculated by constructing an angle of 2° with the xaxis, and then finding the coordinates of the corresponding point (0.9994, 0.0349) on the unit circle. The value of cosec 2° is equal to the reciprocal of the ycoordinate (0.0349). ∴ cosec 2° = 28.6537.
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