TANH

Returns the hyperbolic tangent of an expression.

TANH( numeric-expression )

Usage:

A=TANH(B)

Htangent=TANH(X)

PRINT "Hyperbolic Tangent of";Angle;"=";TANH(Angle)

Example: TANH.BAS

Description:

TANH accepts either a COMPLEX or REAL argument and returns a value of the same type. The argument must be specified in radians, regardless of the current trigonometric mode. The real and imaginary parts of TANH(Z) are calculated (using real arithmetic) as

REAL(TANH(Z)) = SINH(2*REAL(Z))/D

IMAG(TANH(Z)) = SIN(2*IMAG(Z))/D

Where:

D = COSH(2*REAL(Z))+COS(2*IMAG(Z))

The domain of TANH includes all points except CMPLX(0,PI/2+PI*K), where K can be any integer. However, intermediate values generated during the calculation of the function can cause over or underflow errors for very large or small values of Z.

See Also:

ACSH, ASNH, ATNH, COSH, SINH