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Wikipedia: Inverse and hyperbolic trigonometric function
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Hyperbolic Trig functions:
- sinh(x) = (ex - e-x)/2
- cosh(x) = (ex + e-x)/2
- tanh(x) = sinh(x)/cosh(x)
- csch(x) = (sinh(x))-1
- sech(x) = (cosh(x))-1
- coth(x) = cosh(x)/sinh(x)
Inverse Trig functions:
simple definition:
- y = arcsin(x) is equivalent to: x = sin(y) if -pi/2 ? y ? pi/2
- y = arccos(x) is equivalent to: x = cos(y) if 0 ? y ? pi
- y = arctan(x) is equivalent to: x = tan(y) if -pi/2 ? y ? pi/2
- y = arccsc(x) is equivalent to: x = csc(y) if -pi/2 ? y ? pi/2
- y = arcsec(x) is equivalent to: x = sec(y) if 0 ? y ? pi
- y = arccot(x) is equivalent to: x = cot(y) if 0 ? y ? pi (note: ranges need further checking)
calculable definition:
- arcsin(x) = integral with respect to x of((1 - x2)-.5)
- arccos(x) = integral with respect to x of(-1 * (1 - x2)-.5)
- arctan(x) = integral with respect to x of((1 + x2)-1)
- arccsc(x) = integral with respect to x of((-x (x2 - 1).5)-1)
- arcsec(x) = integral with respect to x of((x (x2 - 1).5)-1)
- arccot(x) = integral with respect to x of(-(x2 + 1)<sup>-1)