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.
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
- 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.
- Range – The arccosecant range is between -π2 and π2, excluding 0.
- Monotonicity – In the domain, the arccosecant is monotonically decreasing.
- 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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