Cosec 1410 Degrees
The value of cosec 1410 degrees is -2. Cosec 1410 degrees in radians is written as cosec (1410° × π/180°), i.e., cosec (47π/6) or cosec (24.609142. . .). In this article, we will discuss the methods to find the value of cosec 1410 degrees with examples.
- Cosec 1410°: -2
- Cosec (-1410 degrees): 2
- Cosec 1410° in radians: cosec (47π/6) or cosec (24.6091424 . . .)
What is the Value of Cosec 1410 Degrees?
The value of cosec 1410 degrees is -2. Cosec 1410 degrees can also be expressed using the equivalent of the given angle (1410 degrees) in radians (24.60914 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1410 degrees = 1410° × (π/180°) rad = 47π/6 or 24.6091 . . .
∴ cosec 1410° = cosec(24.6091) = -2
Explanation:
For cosec 1410°, the angle 1410° > 360°. Given the periodic property of the cosecant function, we can represent it as cosec(1410° mod 360°) = cosec(330°). The angle 1410°, coterminal to angle 330°, is located in the Fourth Quadrant(Quadrant IV).
Since cosecant function is negative in the 4th quadrant, thus cosec 1410 degrees value = -2
Similarly, cosec 1410° can also be written as, cosec 1410 degrees = (1410° + n × 360°), n ∈ Z.
⇒ cosec 1410° = cosec 1770° = cosec 2130°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(-1410°) = -cosec(1410°).
Methods to Find Value of Cosec 1410 Degrees
The cosecant function is negative in the 4th quadrant. The value of cosec 1410° is given as -2. We can find the value of cosec 1410 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cosec 1410° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec 1410 degrees as:
- ± 1/√(1-cos²(1410°))
- ± √(1 + tan²(1410°))/tan 1410°
- ± √(1 + cot²(1410°))
- ± sec 1410°/√(sec²(1410°) - 1)
- 1/sin 1410°
Note: Since 1410° lies in the 4th Quadrant, the final value of cosec 1410° will be negative.
We can use trigonometric identities to represent cosec 1410° as,
- cosec(180° - 1410°) = cosec(-1230°)
- -cosec(180° + 1410°) = -cosec 1590°
- sec(90° - 1410°) = sec(-1320°)
- -sec(90° + 1410°) = -sec 1500°
Cosec 1410 Degrees Using Unit Circle
To find the value of cosec 1410 degrees using the unit circle, represent 1410° in the form (3 × 360°) + 330° [∵ 1410°>360°] ∵ cosecant is a periodic function, cosec 1410° = cosec 330°.
- Rotate ‘r’ anticlockwise to form 330° or 1410° angle with the positive x-axis.
- The cosec of 1410 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 1410° = 1/y = -2
☛ Also Check:
FAQs on Cosec 1410 Degrees
What is Cosec 1410 Degrees?
Cosec 1410 degrees is the value of cosecant trigonometric function for an angle equal to 1410 degrees. The value of cosec 1410° is -2.
What is the Value of Cosec 1410 Degrees in Terms of Cot 1410°?
We can represent the cosec function in terms of the cotangent function using trig identities, cosec 1410° can be written as -√(1 + cot²(1410°)). Here, the value of cot 1410° is equal to -1.7321.
What is the Value of Cosec 1410° in Terms of Sec 1410°?
Since the cosec function can be represented using the secant function, we can write cosec 1410° as -sec 1410°/√(sec²(1410°) - 1). The value of sec 1410° is equal to 1.1547.
How to Find Cosec 1410° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cosec 1410° can be given in terms of other trigonometric functions as:
- ± 1/√(1-cos²(1410°))
- ± √(1 + tan²(1410°))/tan 1410°
- ± √(1 + cot²(1410°))
- ± sec 1410°/√(sec²(1410°) - 1)
- 1/sin 1410°
☛ Also check: trigonometric table
How to Find the Value of Cosec 1410 Degrees?
The value of cosec 1410 degrees can be calculated by constructing an angle of 1410° 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 1410° is equal to the reciprocal of the y-coordinate (-0.5). ∴ cosec 1410° = -2.