Cosec 1110 Degrees
The value of cosec 1110 degrees is 2. Cosec 1110 degrees in radians is written as cosec (1110° × π/180°), i.e., cosec (37π/6) or cosec (19.373154. . .). In this article, we will discuss the methods to find the value of cosec 1110 degrees with examples.
- Cosec 1110°: 2
- Cosec (-1110 degrees): -2
- Cosec 1110° in radians: cosec (37π/6) or cosec (19.3731546 . . .)
What is the Value of Cosec 1110 Degrees?
The value of cosec 1110 degrees is 2. Cosec 1110 degrees can also be expressed using the equivalent of the given angle (1110 degrees) in radians (19.37315 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1110 degrees = 1110° × (π/180°) rad = 37π/6 or 19.3731 . . .
∴ cosec 1110° = cosec(19.3731) = 2
Explanation:
For cosec 1110°, the angle 1110° > 360°. Given the periodic property of the cosecant function, we can represent it as cosec(1110° mod 360°) = cosec(30°). The angle 1110°, coterminal to angle 30°, is located in the First Quadrant(Quadrant I).
Since cosecant function is positive in the 1st quadrant, thus cosec 1110 degrees value = 2
Similarly, cosec 1110° can also be written as, cosec 1110 degrees = (1110° + n × 360°), n ∈ Z.
⇒ cosec 1110° = cosec 1470° = cosec 1830°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(-1110°) = -cosec(1110°).
Methods to Find Value of Cosec 1110 Degrees
The cosecant function is positive in the 1st quadrant. The value of cosec 1110° is given as 2. We can find the value of cosec 1110 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cosec 1110 Degrees Using Unit Circle
To find the value of cosec 1110 degrees using the unit circle, represent 1110° in the form (3 × 360°) + 30° [∵ 1110°>360°] ∵ cosecant is a periodic function, cosec 1110° = cosec 30°.
- Rotate ‘r’ anticlockwise to form 30° or 1110° angle with the positive x-axis.
- The cosec of 1110 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 1110° = 1/y = 2
Cosec 1110° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec 1110 degrees as:
- ± 1/√(1-cos²(1110°))
- ± √(1 + tan²(1110°))/tan 1110°
- ± √(1 + cot²(1110°))
- ± sec 1110°/√(sec²(1110°) - 1)
- 1/sin 1110°
Note: Since 1110° lies in the 1st Quadrant, the final value of cosec 1110° will be positive.
We can use trigonometric identities to represent cosec 1110° as,
- cosec(180° - 1110°) = cosec(-930°)
- -cosec(180° + 1110°) = -cosec 1290°
- sec(90° - 1110°) = sec(-1020°)
- -sec(90° + 1110°) = -sec 1200°
☛ Also Check:
FAQs on Cosec 1110 Degrees
What is Cosec 1110 Degrees?
Cosec 1110 degrees is the value of cosecant trigonometric function for an angle equal to 1110 degrees. The value of cosec 1110° is 2.
How to Find Cosec 1110° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cosec 1110° can be given in terms of other trigonometric functions as:
- ± 1/√(1-cos²(1110°))
- ± √(1 + tan²(1110°))/tan 1110°
- ± √(1 + cot²(1110°))
- ± sec 1110°/√(sec²(1110°) - 1)
- 1/sin 1110°
☛ Also check: trigonometry table
What is the Value of Cosec 1110° in Terms of Sec 1110°?
Since the cosec function can be represented using the secant function, we can write cosec 1110° as sec 1110°/√(sec²(1110°) - 1). The value of sec 1110° is equal to 1.1547.
What is the Value of Cosec 1110 Degrees in Terms of Tan 1110°?
We know, using trig identities, we can write cosec 1110° as √(1 + tan²(1110°))/tan 1110°. Here, the value of tan 1110° is equal to 0.5774.
How to Find the Value of Cosec 1110 Degrees?
The value of cosec 1110 degrees can be calculated by constructing an angle of 1110° 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 1110° is equal to the reciprocal of the y-coordinate (0.5). ∴ cosec 1110° = 2.