Cosec 30 Degrees

The value of cosec 30 degrees is 2. Cosec 30 degrees in radians is written as cosec (30° × π/180°), i.e., cosec (π/6) or cosec (0.523598. . .). In this article, we will discuss the methods to find the value of cosec 30 degrees with examples.

• Cosec 30°: 2
• Cosec (-30 degrees): -2
• Cosec 30° in radians: cosec (π/6) or cosec (0.5235987 . . .)

What is the Value of Cosec 30 Degrees?

The value of cosec 30 degrees is 2. Cosec 30 degrees can also be expressed using the equivalent of the given angle (30 degrees) in radians (0.52359 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 30 degrees = 30° × (π/180°) rad = π/6 or 0.5235 . . .
∴ cosec 30° = cosec(0.5235) = 2

Explanation:

For cosec 30 degrees, the angle 30° lies between 0° and 90° (First Quadrant). Since cosecant function is positive in the first quadrant, thus cosec 30° value = 2
Since the cosecant function is a periodic function, we can represent cosec 30° as, cosec 30 degrees = cosec(30° + n × 360°), n ∈ Z.
⇒ cosec 30° = cosec 390° = cosec 750°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(-30°) = -cosec(30°).

Methods to Find Value of Cosec 30 Degrees

The cosecant function is positive in the 1st quadrant. The value of cosec 30° is given as 2. We can find the value of cosec 30 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cosec 30 Degrees Using Unit Circle

To find the value of cosec 30 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 30° angle with the positive x-axis.
• The cosec of 30 degrees 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 30° = 1/y = 2

Cosec 30° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cosec 30 degrees as:

• ± 1/√(1-cos²(30°))
• ± √(1 + tan²(30°))/tan 30°
• ± √(1 + cot²(30°))
• ± sec 30°/√(sec²(30°) - 1)
• 1/sin 30°

Note: Since 30° lies in the 1st Quadrant, the final value of cosec 30° will be positive.

We can use trigonometric identities to represent cosec 30° as,

• cosec(180° - 30°) = cosec 150°
• -cosec(180° + 30°) = -cosec 210°
• sec(90° - 30°) = sec 60°
• -sec(90° + 30°) = -sec 120°

☛ Also Check:

• cosec 90 degrees
• cosec 1200 degrees
• cosec 20 degrees
• cosec 0 degrees
• cosec 30 degrees
• cosec 2 degrees

FAQs on Cosec 30 Degrees

What is Cosec 30 Degrees?

Cosec 30 degrees is the value of cosecant trigonometric function for an angle equal to 30 degrees. The value of cosec 30° is 2.

How to Find the Value of Cosec 30 Degrees?

The value of cosec 30 degrees can be calculated by constructing an angle of 30° with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cosec 30° is equal to the reciprocal of the y-coordinate (0.5). ∴ cosec 30° = 2.

How to Find Cosec 30° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cosec 30° can be given in terms of other trigonometric functions as:

• ± 1/√(1-cos²(30°))
• ± √(1 + tan²(30°))/tan 30°
• ± √(1 + cot²(30°))
• ± sec 30°/√(sec²(30°) - 1)
• 1/sin 30°

☛ Also check: trigonometry table

What is the Value of Csc 30° in Terms of Sin 30°?

Since the cosecant function is the reciprocal of the sine function, we can write csc 30° as 1/sin(30°). The value of sin 30° is equal to 0.5.

What is the Value of Cosec 30 Degrees in Terms of Cot 30°?

We can represent the cosec function in terms of the cotangent function using trig identities, cosec 30° can be written as √(1 + cot²(30°)). Here, the value of cot 30° is equal to 1.7321.