Cosec 20 Degrees

The value of cosec 20 degrees is 2.9238044. . .. Cosec 20 degrees in radians is written as cosec (20° × π/180°), i.e., cosec (π/9) or cosec (0.349065. . .). In this article, we will discuss the methods to find the value of cosec 20 degrees with examples.

• Cosec 20° in decimal: 2.9238044. . .
• Cosec (-20 degrees): -2.9238044. . .
• Cosec 20° in radians: cosec (π/9) or cosec (0.3490658 . . .)

What is the Value of Cosec 20 Degrees?

The value of cosec 20 degrees in decimal is 2.923804400. . .. Cosec 20 degrees can also be expressed using the equivalent of the given angle (20 degrees) in radians (0.34906 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 20 degrees = 20° × (π/180°) rad = π/9 or 0.3490 . . .
∴ cosec 20° = cosec(0.3490) = 2.9238044. . .

Explanation:

For cosec 20 degrees, the angle 20° lies between 0° and 90° (First Quadrant). Since cosecant function is positive in the first quadrant, thus cosec 20° value = 2.9238044. . .
Since the cosecant function is a periodic function, we can represent cosec 20° as, cosec 20 degrees = cosec(20° + n × 360°), n ∈ Z.
⇒ cosec 20° = cosec 380° = cosec 740°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(-20°) = -cosec(20°).

Methods to Find Value of Cosec 20 Degrees

The cosecant function is positive in the 1st quadrant. The value of cosec 20° is given as 2.92380. . .. We can find the value of cosec 20 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cosec 20° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cosec 20 degrees as:

• ± 1/√(1-cos²(20°))
• ± √(1 + tan²(20°))/tan 20°
• ± √(1 + cot²(20°))
• ± sec 20°/√(sec²(20°) - 1)
• 1/sin 20°

Note: Since 20° lies in the 1st Quadrant, the final value of cosec 20° will be positive.

We can use trigonometric identities to represent cosec 20° as,

• cosec(180° - 20°) = cosec 160°
• -cosec(180° + 20°) = -cosec 200°
• sec(90° - 20°) = sec 70°
• -sec(90° + 20°) = -sec 110°

Cosec 20 Degrees Using Unit Circle

To find the value of cosec 20 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 20° angle with the positive x-axis.
• The cosec of 20 degrees equals the reciprocal of the y-coordinate(0.342) of the point of intersection (0.9397, 0.342) of unit circle and r.

Hence the value of cosec 20° = 1/y = 2.9238 (approx)

☛ Also Check:

• cosec 45 degrees
• cosec 150 degrees
• cosec 75 degrees
• cosec 20 degrees
• cosec 0 degrees
• cosec 1110 degrees

FAQs on Cosec 20 Degrees

What is Cosec 20 Degrees?

Cosec 20 degrees is the value of cosecant trigonometric function for an angle equal to 20 degrees. The value of cosec 20° is 2.9238 (approx).

How to Find the Value of Cosec 20 Degrees?

The value of cosec 20 degrees can be calculated by constructing an angle of 20° with the x-axis, and then finding the coordinates of the corresponding point (0.9397, 0.342) on the unit circle. The value of cosec 20° is equal to the reciprocal of the y-coordinate (0.342). ∴ cosec 20° = 2.9238.

What is the Value of Cosec 20 Degrees in Terms of Cot 20°?

We can represent the cosec function in terms of the cotangent function using trig identities, cosec 20° can be written as √(1 + cot²(20°)). Here, the value of cot 20° is equal to 2.7475.

What is the Value of Csc 20° in Terms of Sin 20°?

Since the cosecant function is the reciprocal of the sine function, we can write csc 20° as 1/sin(20°). The value of sin 20° is equal to 0.342.

How to Find Cosec 20° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cosec 20° can be given in terms of other trigonometric functions as:

• ± 1/√(1-cos²(20°))
• ± √(1 + tan²(20°))/tan 20°
• ± √(1 + cot²(20°))
• ± sec 20°/√(sec²(20°) - 1)
• 1/sin 20°

☛ Also check: trigonometry table