Caché Basic Reference Derived Math Functions
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The following non-intrinsic math functions can be derived from the intrinsic 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.