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/√(1-cos²(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 x-axis.
- The cosec of 2 degrees equals the reciprocal of the y-coordinate(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:
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/√(1-cos²(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 x-axis, 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 y-coordinate (0.0349). ∴ cosec 2° = 28.6537.