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Cosec 150 Degrees

The value of cosec 150 degrees is 2. Cosec 150 degrees in radians is written as cosec (150° × π/180°), i.e., cosec (5π/6) or cosec (2.617993. . .). In this article, we will discuss the methods to find the value of cosec 150 degrees with examples.

Cosec 150°: 2
Cosec (-150 degrees): -2
Cosec 150° in radians: cosec (5π/6) or cosec (2.6179938 . . .)

What is the Value of Cosec 150 Degrees?

The value of cosec 150 degrees is 2. Cosec 150 degrees can also be expressed using the equivalent of the given angle (150 degrees) in radians (2.61799 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 150 degrees = 150° × (π/180°) rad = 5π/6 or 2.6179 . . .
∴ cosec 150° = cosec(2.6179) = 2

Explanation:

For cosec 150 degrees, the angle 150° lies between 90° and 180° (Second Quadrant). Since cosecant function is positive in the second quadrant, thus cosec 150° value = 2
Since the cosecant function is a periodic function, we can represent cosec 150° as, cosec 150 degrees = cosec(150° + n × 360°), n ∈ Z.
⇒ cosec 150° = cosec 510° = cosec 870°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(-150°) = -cosec(150°).

Methods to Find Value of Cosec 150 Degrees

The cosecant function is positive in the 2nd quadrant. The value of cosec 150° is given as 2. We can find the value of cosec 150 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cosec 150° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cosec 150 degrees as:

± 1/√(1-cos²(150°))
± √(1 + tan²(150°))/tan 150°
± √(1 + cot²(150°))
± sec 150°/√(sec²(150°) - 1)
1/sin 150°

Note: Since 150° lies in the 2nd Quadrant, the final value of cosec 150° will be positive.

We can use trigonometric identities to represent cosec 150° as,

cosec(180° - 150°) = cosec 30°
-cosec(180° + 150°) = -cosec 330°
sec(90° - 150°) = sec(-60°)
-sec(90° + 150°) = -sec 240°

Cosec 150 Degrees Using Unit Circle

To find the value of cosec 150 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 150° angle with the positive x-axis.
The cosec of 150 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 150° = 1/y = 2

☛ Also Check:

Examples Using Cosec 150 Degrees

Example 1: Simplify: 4 (cosec 150°/cosec 510°)

Solution:

We know cosec 150° = cosec 510°
⇒ 4 cosec 150°/cosec 510° = 4(cosec 150°/cosec 150°)
= 4(1) = 4
Example 2: Using the value of csc 150°, solve: (1 + cot²(150°)).

Solution:
We know, (1 + cot²(150°)) = (csc²(150°)) = 4
⇒ (1 + cot²(150°)) = 4
Example 3: Find the value of 9 cosec(150°)/10 sec(-60°).

Solution:

Using trigonometric identities, we know, cosec(150°) = sec(90° - 150°) = sec(-60°).
⇒ cosec(150°) = sec(-60°)
⇒ Value of 9 cosec(150°)/10 sec(-60°) = 9/10

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FAQs on Cosec 150 Degrees

What is Cosec 150 Degrees?

Cosec 150 degrees is the value of cosecant trigonometric function for an angle equal to 150 degrees. The value of cosec 150° is 2.

How to Find the Value of Cosec 150 Degrees?

The value of cosec 150 degrees can be calculated by constructing an angle of 150° 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 150° is equal to the reciprocal of the y-coordinate (0.5). ∴ cosec 150° = 2.

What is the Value of Cosec 150° in Terms of Sec 150°?

Since the cosec function can be represented using the secant function, we can write cosec 150° as -sec 150°/√(sec²(150°) - 1). The value of sec 150° is equal to -1.1547.

What is the Value of Cosec 150 Degrees in Terms of Cot 150°?

We can represent the cosec function in terms of the cotangent function using trig identities, cosec 150° can be written as √(1 + cot²(150°)). Here, the value of cot 150° is equal to -1.7321.

How to Find Cosec 150° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cosec 150° can be given in terms of other trigonometric functions as:

± 1/√(1-cos²(150°))
± √(1 + tan²(150°))/tan 150°
± √(1 + cot²(150°))
± sec 150°/√(sec²(150°) - 1)
1/sin 150°

☛ Also check: trigonometric table

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