Calculates the hyperbolic tangent of a value.

tanh(*value*)

The tanh( command is only found in the Catalog. Press:

- 2nd CATALOG to access the command catalog.
- T to skip to commands starting with T.
- Scroll down and select tanh(.

TI-83/84/+/SE

1 byte

Calculates the hyperbolic tangent of a value. The hyperbolic trig functions sinh(, cosh(, and tanh( are an analog of normal trig functions, but for a hyperbola, rather than a circle. They can be expressed in terms of real powers of e, and don't depend on the Degree or Radian mode setting.

```
tanh(0)
0
tanh(1)
.761594156
```

Like normal trig commands, tanh( works on lists as well, but not on complex numbers, even though the function is often extended to the complex numbers in mathematics.

# Advanced Uses

The tanh( command can be used to approximate the sign function:

(1)As the absolute value of the input becomes large, the convergence is achieved at a point closer to zero. For the function to work as intended generally, numbers having lesser orders of magnitude need to be multiplied by a factor large enough for the argument to arrive at ±16.720082053122, which is the smallest input to produce ±1 (respectively) to fourteen digits of accuracy.

```
5/12→X
.4166666667
tanh(E9X)
1
tanh(-E9X)
-1
```

# Formulas

The definition of the hyperbolic tangent is:

(2)# Related Commands

.