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# Inverse and hyperbolic trigonometric function

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Hyperbolic Trig functions:

1. sinh(x) = (ex - e-x)/2
2. cosh(x) = (ex + 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) = integral with respect to x of((1 - x2)-.5)
2. arccos(x) = integral with respect to x of(-1 * (1 - x2)-.5)
3. arctan(x) = integral with respect to x of((1 + x2)-1)
4. arccsc(x) = integral with respect to x of((-x (x2 - 1).5)-1)
5. arcsec(x) = integral with respect to x of((x (x2 - 1).5)-1)
6. arccot(x) = integral with respect to x of(-(x2 + 1)<sup>-1)

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Last edited August 16, 2001 12:48 am (diff)
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