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Arccsc Calculator – Find the Exact Value of Inverse Cosecant

The Arccsc Calculator is a free online tool that calculates angles based on the value of cosecant. Angles can be expressed in degrees and radians.

Arccsc Calculator

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What is arccsc?

Arccsc is the abbreviation of arccosecant, which is the inverse function of cosecant. It is one of the six inverse trigonometric functions. The arccsc is a function used to find the size of the angle based on the given ratio of the hypotenuse to the opposite side. Its formula is:

θ = arcsec(hypotenuseopposite)

In addition to arccsc, you can also use csc-1 to represent inverse cosecant.

Arccsc graph and properties

Since the cosecant function is a periodic function, the cosecant function is not a bijective function, so there is no inverse function. To get the inverse of cosecant, we specify the domain of the cosecant function to be between -π2 and π2, excluding 0. The arccsc graph is as follows:

arccosecant graph

arccosecant graph

  1. Domain – The absolute value of the domain of arccosecant is greater than or equal to 1. That is, less than or equal to -1 or greater than or equal to 1.
  2. Range – The arccosecant range is between -π2 and π2, excluding 0.
  3. Monotonicity – In the domain, the arccosecant is monotonically decreasing.
  4. Odd function – Since arccsc(x) = -arccsc(-x), the arccosecant is an odd function.

How to calculate arccsc?

The easiest way to calculate the arccsc is to use the inverse cosecant calculator. Because the inverse cosecant is difficult to calculate by hand. Some people may use the arccosecant table (given below) to find the corresponding angle, but the inverse cosecant table has obvious defects. It is impossible to list all inverse cosecant values. When encountering a value that doesn’t exist in the inverse cosecant table, there’s nothing you can do about it. So, using an inverse cosecant calculator is the best option.

Arccsc(x) Degrees Radians
-1 -90° -π2
-1.00015233 -89° -89π180
-1.00060954 -88° -22π45
-1.00137235 -87° -29π60
-1.0024419 -86° -43π90
-1.00381984 -85° -17π36
-1.00550828 -84° -7π15
-1.00750983 -83° -83π180
-1.00982757 -82° -41π90
-1.01246513 -81° -9π20
-1.01542661 -80° -4π9
-1.01871669 -79° -79π180
-1.02234059 -78° -13π30
-1.02630411 -77° -77π180
-1.03061363 -76° -19π45
-1.03527618 -75° -5π12
-1.04029944 -74° -37π90
-1.04569176 -73° -73π180
-1.05146222 -72° -2π5
-1.05762068 -71° -71π180
-1.06417777 -70° -7π18
-1.07114499 -69° -23π60
-1.07853474 -68° -17π45
-1.08636038 -67° -67π180
-1.09463628 -66° -11π30
-1.10337792 -65° -13π36
-1.11260194 -64° -16π45
-1.12232624 -63° -7π20
-1.13257005 -62° -31π90
-1.14335407 -61° -61π180
-1.15470054 -60° -π3
-1.1666334 -59° -59π180
-1.1791784 -58° -29π90
-1.19236329 -57° -19π60
-1.20621795 -56° -14π45
-1.22077459 -55° -11π36
-1.23606798 -54° -3π10
-1.25213566 -53° -53π180
-1.26901822 -52° -13π45
-1.28675957 -51° -17π60
-1.30540729 -50° -5π18
-1.32501299 -49° -49π180
-1.34563273 -48° -4π15
-1.36732746 -47° -47π180
-1.39016359 -46° -23π90
-1.41421356 -45° -π4
-1.43955654 -44° -11π45
-1.46627919 -43° -43π180
-1.49447655 -42° -7π30
-1.52425309 -41° -41π180
-1.55572383 -40° -2π9
-1.58901573 -39° -13π60
-1.62426925 -38° -19π90
-1.66164014 -37° -37π180
-1.70130162 -36° -π5
-1.7434468 -35° -7π36
-1.78829165 -34° -17π90
-1.83607846 -33° -11π60
-1.88707991 -32° -8π45
-1.94160403 -31° -31π180
-2 -30° -π6
-2.06266534 -29° -29π180
-2.13005447 -28° -7π45
-2.20268926 -27° -3π20
-2.28117203 -26° -13π90
-2.36620158 -25° -5π36
-2.45859334 -24° -2π15
-2.55930467 -23° -23π180
-2.66946716 -22° -11π90
-2.79042811 -21° -7π60
-2.9238044 -20° -π9
-3.07155349 -19° -19π180
-3.23606798 -18° -π10
-3.42030362 -17° -17π180
-3.62795528 -16° -4π45
-3.86370331 -15° -π12
-4.13356549 -14° -7π90
-4.44541148 -13° -13π180
-4.80973434 -12° -π15
-5.24084306 -11° -11π180
-5.75877048 -10° -π18
-6.39245322 -9° -π20
-7.18529653 -8° -2π45
-8.20550905 -7° -7π180
-9.56677223 -6° -π30
-11.47371325 -5° -π36
-14.33558703 -4° -π45
-19.10732261 -3° -π60
-28.65370835 -2° -π90
-57.2986885 -1° -π180
57.2986885 1° π180
28.65370835 2° π90
19.10732261 3° π60
14.33558703 4° π45
11.47371325 5° π36
9.56677223 6° π30
8.20550905 7° 7π180
7.18529653 8° 2π45
6.39245322 9° π20
5.75877048 10° π18
5.24084306 11° 11π180
4.80973434 12° π15
4.44541148 13° 13π180
4.13356549 14° 7π90
3.86370331 15° π12
3.62795528 16° 4π45
3.42030362 17° 17π180
3.23606798 18° π10
3.07155349 19° 19π180
2.9238044 20° π9
2.79042811 21° 7π60
2.66946716 22° 11π90
2.55930467 23° 23π180
2.45859334 24° 2π15
2.36620158 25° 5π36
2.28117203 26° 13π90
2.20268926 27° 3π20
2.13005447 28° 7π45
2.06266534 29° 29π180
2 30° π6
1.94160403 31° 31π180
1.88707991 32° 8π45
1.83607846 33° 11π60
1.78829165 34° 17π90
1.7434468 35° 7π36
1.70130162 36° π5
1.66164014 37° 37π180
1.62426925 38° 19π90
1.58901573 39° 13π60
1.55572383 40° 2π9
1.52425309 41° 41π180
1.49447655 42° 7π30
1.46627919 43° 43π180
1.43955654 44° 11π45
1.41421356 45° π4
1.39016359 46° 23π90
1.36732746 47° 47π180
1.34563273 48° 4π15
1.32501299 49° 49π180
1.30540729 50° 5π18
1.28675957 51° 17π60
1.26901822 52° 13π45
1.25213566 53° 53π180
1.23606798 54° 3π10
1.22077459 55° 11π36
1.20621795 56° 14π45
1.19236329 57° 19π60
1.1791784 58° 29π90
1.1666334 59° 59π180
1.15470054 60° π3
1.14335407 61° 61π180
1.13257005 62° 31π90
1.12232624 63° 7π20
1.11260194 64° 16π45
1.10337792 65° 13π36
1.09463628 66° 11π30
1.08636038 67° 67π180
1.07853474 68° 17π45
1.07114499 69° 23π60
1.06417777 70° 7π18
1.05762068 71° 71π180
1.05146222 72° 2π5
1.04569176 73° 73π180
1.04029944 74° 37π90
1.03527618 75° 5π12
1.03061363 76° 19π45
1.02630411 77° 77π180
1.02234059 78° 13π30
1.01871669 79° 79π180
1.01542661 80° 4π9
1.01246513 81° 9π20
1.00982757 82° 41π90
1.00750983 83° 83π180
1.00550828 84° 7π15
1.00381984 85° 17π36
1.0024419 86° 43π90
1.00137235 87° 29π60
1.00060954 88° 22π45
1.00015233 89° 89π180
1 90° π2

How to use this arccsc calculator

The arccsc calculator is easy to use. Just enter the value and click the calculation button. This value can be an integer, decimal or fraction. If entering a fraction, remember to separate the numerator and denominator with /.

FAQS

  • Q: When to use inverse cosecant?
    A: In a right triangle, when the ratio of the hypotenuse side to the opposite side of the acute angle is known, to calculate the angle, the arccosecant can be considered.
  • Q: Are arccsc and csc^-1 the same?
    A: Yes, they are both inverse cosecant.
  • Q: Is inverse cosecant the same as sine?
    A: No. Sine is the reciprocal of cosecant, not the same as the inverse cosecant.
  • Q: Why does the arcsec calculator calculate an error?
    A: In one case, the entered value is outside the inverse cosecant domain. Therefore, the calculation cannot find a result or an error occurs, etc. The domains of arccosecant are (-∞,-1] and [1, +∞).
  • Q: What is the inverse cosecant of 2?
    A: The inverse cosecant of 2 is 30 degrees, which is π6.

    arccsc(2) = 30°

  • Q: What is the inverse cosecant of root 2?
    A: The inverse cosecant of root 2 is 45 degrees, which is π4.

    arccsc(√2) = 45°

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