Difference between revisions of "Hyperbolic trig functions"
m |
|||
| Line 7: | Line 7: | ||
<math>\tanh(x)= \frac{\sinh{x}}{\cosh{x}} =\frac{e^x+e^{-x}}{e^x-e^{-x}}</math> | <math>\tanh(x)= \frac{\sinh{x}}{\cosh{x}} =\frac{e^x+e^{-x}}{e^x-e^{-x}}</math> | ||
| − | + | They behave much like normal trig functions, as most of the identities still hold. | |
| + | They do so because: | ||
<math>\sinh(x)= -i\sin{ix}</math> | <math>\sinh(x)= -i\sin{ix}</math> | ||
| Line 16: | Line 17: | ||
<math>\tanh(x)= -1\tan{iz}</math> | <math>\tanh(x)= -1\tan{iz}</math> | ||
| + | |||
| + | However, the arc-hyperbolic trig functions have different derivatives. | ||
{{stub}} | {{stub}} | ||
Latest revision as of 20:00, 3 November 2024
The Hyperbolic trig functions can be thought of the classical trig functions except found on an unit hyperbola. There are as follows:
They behave much like normal trig functions, as most of the identities still hold. They do so because:
However, the arc-hyperbolic trig functions have different derivatives.
This article is a stub. Help us out by expanding it.
