Inverse and hyperbolic trigonometric function

Hyperbolic Trig functions:

1. sinh(x) = (e^x - e^-x)/2
2. cosh(x) = (e^x + e^-x)/2
3. tanh(x) = sinh(x)/cosh(x)
4. csch(x) = (sinh(x))^-1
5. sech(x) = (cosh(x))^-1
6. coth(x) = cosh(x)/sinh(x)

Inverse Trig functions: simple definition:

1. y = arcsin(x) is equivalent to: x = sin(y) if -pi/2 ≤ y ≤ pi/2
2. y = arccos(x) is equivalent to: x = cos(y) if 0 ≤ y ≤ pi
3. y = arctan(x) is equivalent to: x = tan(y) if -pi/2 ≤ y ≤ pi/2
4. y = arccsc(x) is equivalent to: x = csc(y) if -pi/2 ≤ y ≤ pi/2
5. y = arcsec(x) is equivalent to: x = sec(y) if 0 ≤ y ≤ pi
6. y = arccot(x) is equivalent to: x = cot(y) if 0 ≤ y ≤ pi (note: ranges need further checking)

calculable definition:

1. arcsin(x) = ∫(1 - x²)^-.5dx
2. arccos(x) = ∫-(1 - x²)^-.5dx
3. arctan(x) = ∫(1 + x²)^-1dx
4. arccsc(x) = ∫(-x (x² - 1)^.5)^-1dx
5. arcsec(x) = ∫(x (x² - 1)^.5)^-1dx
6. arccot(x) = ∫-(x² + 1)^-1dx