Difference between revisions of "Hyperbolic trig functions"
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The Hyperbolic trig functions can be thought of the classical trig functions except found on an unit hyperbola. There are as follows: | The Hyperbolic trig functions can be thought of the classical trig functions except found on an unit hyperbola. There are as follows: | ||
− | <math>e^x+e^-x</math> | + | |
+ | <math>\sinh(x)=\frac{e^x+e^{-x}}{2}</math> | ||
+ | |||
+ | <math>\cosh(x)=\frac{e^x-e^{-x}}{2}</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>\cosh(x)=\cos{iz}</math> | ||
+ | |||
+ | |||
+ | <math>\tanh(x)= -1\tan{iz}</math> | ||
+ | |||
+ | However, the arc-hyperbolic trig functions have different derivatives. | ||
+ | |||
+ | {{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.
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