Cosec 240 Degrees
The value of cosec 240 degrees is -1.1547005. . .. Cosec 240 degrees in radians is written as cosec (240° × π/180°), i.e., cosec (4π/3) or cosec (4.188790. . .). In this article, we will discuss the methods to find the value of cosec 240 degrees with examples.
- Cosec 240°: -2/√3
- Cosec 240° in decimal: -1.1547005. . .
- Cosec (-240 degrees): 1.1547005. . . or 2/√3
- Cosec 240° in radians: cosec (4π/3) or cosec (4.1887902 . . .)
What is the Value of Cosec 240 Degrees?
The value of cosec 240 degrees in decimal is -1.154700538. . .. Cosec 240 degrees can also be expressed using the equivalent of the given angle (240 degrees) in radians (4.18879 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 240 degrees = 240° × (π/180°) rad = 4π/3 or 4.1887 . . .
∴ cosec 240° = cosec(4.1887) = -2/√3 or -1.1547005. . .
Explanation:
For cosec 240 degrees, the angle 240° lies between 180° and 270° (Third Quadrant). Since cosecant function is negative in the third quadrant, thus cosec 240° value = -2/√3 or -1.1547005. . .
Since the cosecant function is a periodic function, we can represent cosec 240° as, cosec 240 degrees = cosec(240° + n × 360°), n ∈ Z.
⇒ cosec 240° = cosec 600° = cosec 960°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(-240°) = -cosec(240°).
Methods to Find Value of Cosec 240 Degrees
The cosecant function is negative in the 3rd quadrant. The value of cosec 240° is given as -1.15470. . .. We can find the value of cosec 240 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cosec 240° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec 240 degrees as:
- ± 1/√(1-cos²(240°))
- ± √(1 + tan²(240°))/tan 240°
- ± √(1 + cot²(240°))
- ± sec 240°/√(sec²(240°) - 1)
- 1/sin 240°
Note: Since 240° lies in the 3rd Quadrant, the final value of cosec 240° will be negative.
We can use trigonometric identities to represent cosec 240° as,
- cosec(180° - 240°) = cosec(-60°)
- -cosec(180° + 240°) = -cosec 420°
- sec(90° - 240°) = sec(-150°)
- -sec(90° + 240°) = -sec 330°
Cosec 240 Degrees Using Unit Circle
To find the value of cosec 240 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 240° angle with the positive x-axis.
- The cosec of 240 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 240° = 1/y = -1.1547 (approx)
☛ Also Check:
FAQs on Cosec 240 Degrees
What is Cosec 240 Degrees?
Cosec 240 degrees is the value of cosecant trigonometric function for an angle equal to 240 degrees. The value of cosec 240° is -2/√3 or -1.1547 (approx).
How to Find Cosec 240° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cosec 240° can be given in terms of other trigonometric functions as:
- ± 1/√(1-cos²(240°))
- ± √(1 + tan²(240°))/tan 240°
- ± √(1 + cot²(240°))
- ± sec 240°/√(sec²(240°) - 1)
- 1/sin 240°
☛ Also check: trigonometry table
What is the Value of Cosec 240° in Terms of Sec 240°?
Since the cosec function can be represented using the secant function, we can write cosec 240° as sec 240°/√(sec²(240°) - 1). The value of sec 240° is equal to -2.
How to Find the Value of Cosec 240 Degrees?
The value of cosec 240 degrees can be calculated by constructing an angle of 240° 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 240° is equal to the reciprocal of the y-coordinate (-0.866). ∴ cosec 240° = -1.1547.
What is the Value of Cosec 240 Degrees in Terms of Cot 240°?
We can represent the cosec function in terms of the cotangent function using trig identities, cosec 240° can be written as -√(1 + cot²(240°)). Here, the value of cot 240° is equal to 0.5774.