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Cosec 1200 Degrees

The value of cosec 1200 degrees is 1.1547005. . .. Cosec 1200 degrees in radians is written as cosec (1200° × π/180°), i.e., cosec (20π/3) or cosec (20.943951. . .). In this article, we will discuss the methods to find the value of cosec 1200 degrees with examples.

Cosec 1200°: 2/√3
Cosec 1200° in decimal: 1.1547005. . .
Cosec (-1200 degrees): -1.1547005. . . or -2/√3
Cosec 1200° in radians: cosec (20π/3) or cosec (20.9439510 . . .)

What is the Value of Cosec 1200 Degrees?

The value of cosec 1200 degrees in decimal is 1.154700538. . .. Cosec 1200 degrees can also be expressed using the equivalent of the given angle (1200 degrees) in radians (20.94395 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1200 degrees = 1200° × (π/180°) rad = 20π/3 or 20.9439 . . .
∴ cosec 1200° = cosec(20.9439) = 2/√3 or 1.1547005. . .

Explanation:

For cosec 1200°, the angle 1200° > 360°. Given the periodic property of the cosecant function, we can represent it as cosec(1200° mod 360°) = cosec(120°). The angle 1200°, coterminal to angle 120°, is located in the Second Quadrant(Quadrant II).
Since cosecant function is positive in the 2nd quadrant, thus cosec 1200 degrees value = 2/√3 or 1.1547005. . .
Similarly, cosec 1200° can also be written as, cosec 1200 degrees = (1200° + n × 360°), n ∈ Z.
⇒ cosec 1200° = cosec 1560° = cosec 1920°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(-1200°) = -cosec(1200°).

Methods to Find Value of Cosec 1200 Degrees

The cosecant function is positive in the 2nd quadrant. The value of cosec 1200° is given as 1.15470. . .. We can find the value of cosec 1200 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cosec 1200° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cosec 1200 degrees as:

± 1/√(1-cos²(1200°))
± √(1 + tan²(1200°))/tan 1200°
± √(1 + cot²(1200°))
± sec 1200°/√(sec²(1200°) - 1)
1/sin 1200°

Note: Since 1200° lies in the 2nd Quadrant, the final value of cosec 1200° will be positive.

We can use trigonometric identities to represent cosec 1200° as,

cosec(180° - 1200°) = cosec(-1020°)
-cosec(180° + 1200°) = -cosec 1380°
sec(90° - 1200°) = sec(-1110°)
-sec(90° + 1200°) = -sec 1290°

Cosec 1200 Degrees Using Unit Circle

To find the value of cosec 1200 degrees using the unit circle, represent 1200° in the form (3 × 360°) + 120° [∵ 1200°>360°] ∵ cosecant is a periodic function, cosec 1200° = cosec 120°.

Rotate ‘r’ anticlockwise to form 120° or 1200° angle with the positive x-axis.
The cosec of 1200 degrees equals the reciprocal of the y-coordinate(0.866) of the point of intersection (-0.5, 0.866) of unit circle and r.

Hence the value of cosec 1200° = 1/y = 1.1547 (approx)

☛ Also Check:

Examples Using Cosec 1200 Degrees

Example 1: Find the value of csc 1200° if sin 1200° is 0.8660.

Solution:
Since, csc 1200° = 1/sin 1200°
⇒ csc 1200° = 1/0.8660 = 1.1547
Example 2: Find the value of (sec 600° cosec 600°)/2. [Hint: Use cosec 1200° = 1.1547]

Solution:

Using the sin 2a formula,
(sec 600° cosec 600°)/2 = 1/(2 × cos 600° sin 600°) = 1/sin 1200°
= 1/sin 1200° = cosec 1200° = 1.1547
⇒ (sec 600° cosec 600°)/2 = 1.1547
Example 3: Simplify: 8 (cosec 1200°/cosec 2640°)

Solution:

We know cosec 1200° = cosec 2640°
⇒ 8 cosec 1200°/cosec 2640° = 8(cosec 1200°/cosec 1200°)
= 8(1) = 8

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FAQs on Cosec 1200 Degrees

What is Cosec 1200 Degrees?

Cosec 1200 degrees is the value of cosecant trigonometric function for an angle equal to 1200 degrees. The value of cosec 1200° is 2/√3 or 1.1547 (approx).

What is the Value of Cosec 1200° in Terms of Sec 1200°?

Since the cosec function can be represented using the secant function, we can write cosec 1200° as -sec 1200°/√(sec²(1200°) - 1). The value of sec 1200° is equal to -2.

What is the Value of Cosec 1200 Degrees in Terms of Tan 1200°?

We know, using trig identities, we can write cosec 1200° as -√(1 + tan²(1200°))/tan 1200°. Here, the value of tan 1200° is equal to -1.7321.

How to Find the Value of Cosec 1200 Degrees?

The value of cosec 1200 degrees can be calculated by constructing an angle of 1200° with the x-axis, and then finding the coordinates of the corresponding point (-0.5, 0.866) on the unit circle. The value of cosec 1200° is equal to the reciprocal of the y-coordinate (0.866). ∴ cosec 1200° = 1.1547.

How to Find Cosec 1200° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cosec 1200° can be given in terms of other trigonometric functions as:

± 1/√(1-cos²(1200°))
± √(1 + tan²(1200°))/tan 1200°
± √(1 + cot²(1200°))
± sec 1200°/√(sec²(1200°) - 1)
1/sin 1200°

☛ Also check: trigonometry table

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