Cosec 210 Degrees

The value of cosec 210 degrees is -2. Cosec 210 degrees in radians is written as cosec (210° × π/180°), i.e., cosec (7π/6) or cosec (3.665191. . .). In this article, we will discuss the methods to find the value of cosec 210 degrees with examples.

• Cosec 210°: -2
• Cosec (-210 degrees): 2
• Cosec 210° in radians: cosec (7π/6) or cosec (3.6651914 . . .)

What is the Value of Cosec 210 Degrees?

The value of cosec 210 degrees is -2. Cosec 210 degrees can also be expressed using the equivalent of the given angle (210 degrees) in radians (3.66519 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 210 degrees = 210° × (π/180°) rad = 7π/6 or 3.6651 . . .
∴ cosec 210° = cosec(3.6651) = -2

Explanation:

For cosec 210 degrees, the angle 210° lies between 180° and 270° (Third Quadrant). Since cosecant function is negative in the third quadrant, thus cosec 210° value = -2
Since the cosecant function is a periodic function, we can represent cosec 210° as, cosec 210 degrees = cosec(210° + n × 360°), n ∈ Z.
⇒ cosec 210° = cosec 570° = cosec 930°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(-210°) = -cosec(210°).

Methods to Find Value of Cosec 210 Degrees

The cosecant function is negative in the 3rd quadrant. The value of cosec 210° is given as -2. We can find the value of cosec 210 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cosec 210° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cosec 210 degrees as:

• ± 1/√(1-cos²(210°))
• ± √(1 + tan²(210°))/tan 210°
• ± √(1 + cot²(210°))
• ± sec 210°/√(sec²(210°) - 1)
• 1/sin 210°

Note: Since 210° lies in the 3rd Quadrant, the final value of cosec 210° will be negative.

We can use trigonometric identities to represent cosec 210° as,

• cosec(180° - 210°) = cosec(-30°)
• -cosec(180° + 210°) = -cosec 390°
• sec(90° - 210°) = sec(-120°)
• -sec(90° + 210°) = -sec 300°

Cosec 210 Degrees Using Unit Circle

To find the value of cosec 210 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 210° angle with the positive x-axis.
• The cosec of 210 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 210° = 1/y = -2

☛ Also Check:

• cosec 0 degrees
• cosec 45 degrees
• cosec 75 degrees
• cosec 30 degrees
• cosec 1200 degrees
• cosec 2 degrees

FAQs on Cosec 210 Degrees

What is Cosec 210 Degrees?

Cosec 210 degrees is the value of cosecant trigonometric function for an angle equal to 210 degrees. The value of cosec 210° is -2.

How to Find Cosec 210° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cosec 210° can be given in terms of other trigonometric functions as:

• ± 1/√(1-cos²(210°))
• ± √(1 + tan²(210°))/tan 210°
• ± √(1 + cot²(210°))
• ± sec 210°/√(sec²(210°) - 1)
• 1/sin 210°

☛ Also check: trigonometry table

What is the Exact Value of Cosec 210 Degrees?

The exact value of cosec 210 degrees is -2.

How to Find the Value of Cosec 210 Degrees?

The value of cosec 210 degrees can be calculated by constructing an angle of 210° 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 210° is equal to the reciprocal of the y-coordinate (-0.5). ∴ cosec 210° = -2.

What is the Value of Csc 210 Degrees in Terms of Cos 210°?

Using trigonometric identities, we can write csc 210° in terms of cos 210° as, csc(210°) = -1/√(1 - cos²(210°)). Here, the value of cos 210° is equal to -0.866.