Derived Math Functions
Description
Caché Basic supplies four trigonometric functions: Sin (sine), Cos (cosine), Tan (tangent), and Atn (arctangent); two logarithmic functions: Log (natural e logarithm) and Exp (e exponential); the Sqr (square root) function and the Sgn (sign) function. From these many other functions and constants can be derived.
| Function | Derived Equivalents |
|---|---|
| Secant | Sec(X) = 1 / Cos(X) |
| Cosecant | Cosec(X) = 1 / Sin(X) |
| Cotangent | Cotan(X) = 1 / Tan(X) |
| Inverse Sine | Arcsin(X) = Atn(X / Sqr(-X * X + 1)) |
| Inverse Cosine | Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1) |
| Inverse Secant | Arcsec(X) = Atn(X / Sqr(X * X - 1)) + Sgn((X) -1) * (2 * Atn(1)) |
| Inverse Cosecant | Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1)) |
| Inverse Cotangent | Arccotan(X) = Atn(X) + 2 * Atn(1) |
| Hyperbolic Sine | HSin(X) = (Exp(X) - Exp(-X)) / 2 |
| Hyperbolic Cosine | HCos(X) = (Exp(X) + Exp(-X)) / 2 |
| Hyperbolic Tangent | HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X)) |
| Hyperbolic Secant | HSec(X) = 2 / (Exp(X) + Exp(-X)) |
| Hyperbolic Cosecant | HCosec(X) = 2 / (Exp(X) - Exp(-X)) |
| Hyperbolic Cotangent | HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X)) |
| Inverse Hyperbolic Sine | HArcsin(X) = Log(X + Sqr(X * X + 1)) |
| Inverse Hyperbolic Cosine | HArccos(X) = Log(X + Sqr(X * X - 1)) |
| Inverse Hyperbolic Tangent | HArctan(X) = Log((1 + X) / (1 - X)) / 2 |
| Inverse Hyperbolic Secant | HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X) |
| Inverse Hyperbolic Cosecant | HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) +1) / X) |
| Inverse Hyperbolic Cotangent | HArccotan(X) = Log((X + 1) / (X - 1)) / 2 |
| Base-10 Logarithm | Log10(X) = Log(X) / Log(10) |
| Logarithm to base N | LogN(X) = Log(X) / Log(N) |
ObjectScript Equivalents
ObjectScript supplies the following nine trigonometric functions: $ZSIN sine function; $ZCOS cosine function; $ZARCSIN inverse (arc) sine function; $ZARCCOS inverse (arc) cosine function; $ZTAN tangent function; $ZARCTAN inverse (arc) tangent function; $ZCOT cotangent function; $ZSEC secant function; and $ZCSC cosecant function.
ObjectScript supplies the following three logarithmic functions: $ZEXP e exponential function; $ZLN natural logarithm function; and $ZLOG base-10 logarithm function.
ObjectScript supplies the following two exponential functions: $ZPOWER exponent function; and $ZSQR square root function.
