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Calculate the inverse cosecant (arccsc) of a value. Find the angle whose cosecant equals the input.
| x | arccsc(x) in Degrees | arccsc(x) in Radians |
|---|---|---|
| -2 | -30° | -π/6 |
| -1.414 | -45° | -π/4 |
| -1.155 | -60° | -π/3 |
| -1 | -90° | -π/2 |
| 1 | 90° | π/2 |
| 1.155 | 60° | π/3 |
| 1.414 | 45° | π/4 |
| 2 | 30° | π/6 |
arccsc(x) = arcsin(1/x)
d/dx[arccsc(x)] = -1/(|x|√(x²-1))
Odd function: arccsc(-x) = -arccsc(x)
arccsc(x) = arcsin(1/x)
Because csc(θ) = 1/sin(θ), and since |sin(θ)| ≤ 1, we have |csc(θ)| ≥ 1. So there's no angle whose cosecant is between -1 and 1.
Use arccsc(x) = arcsin(1/x). Just take 1/x and use the arcsin function.
Because csc(0) is undefined (sin(0) = 0, so 1/sin(0) is undefined). The angle 0 has no cosecant value.