什麼是雙曲函數:sinh,cosh,tanh

sinh(x)=(e^x-e^(-x))/2
cosh(x)=(e^x+e^(-x))/2
tanh(x)=sinh(x)/cosh(x)
d(sinh(x)/dx=cosh(x)
d(cosh(x)/dx=sinh(x)
....
cosh(x)^2-sinh(x)^2=1
So there are many similarities with the trigonometric functions.
For details, see:

http://zh.wikipedia.org/wiki/%E5%8F%8C%E6%9B%B2%E5%87%BD%E6%95%B0