Commodore 64 - Deriving Mathematical Functions

APPENDIX H
DERIVING MATHEMATICAL FUNCTIONS
Functions that are not intrinsic to Commodore 64 BASIC may be calcu-
lated as follows:
'140
FUNCTION
BASIC EQUIVALENT
SECANT
SEC(X)= I/COS(X)
COSECANT
CSC(X)= I/SIN(X)
COTANGENT
COT(X)= I/TAN(X)
INVERSESINE
ARCSIN(X)=ATN(X/SQR(- X.X + 1»
INVERSECOSINE
ARCCOS(X)= -ATN(X/SQR
(-X.X +1» +7T/2
INVERSESECANT
ARCSEC(X)=ATN(X/SQR(X.X - 1»
INVERSECOSECANT
ARCCSC(X)=ATN(X/SQR(X.X -1»
+(SGN(X)-I.7T/2
INVERSECOTANGENT
ARCOT(X)=ATN(X)+7T/2
HYPERBOLIC SINE
SINH(X)= (EXP(X)- EXP(- X»/2
HYPERBOLIC COSINE
COSH(X)= (EXP(X)+ EXP( - X»/2
HYPERBOLICTANGENT
TAN H(X)= EXP( - X)/(EXP(x)+ EXP
(- X».2+ 1
HYPERBOLIC SECANT
SECH(X)= 2/(EXP(X)+ EXP( - X»
HYPERBOLIC COSECANT
CSCH(X)= 2/(EXP(X)- EXP(- X»
HYPERBOLIC COTANGENT
COTH(X)= EXP( - X)/(EXP(X)
-EXP(-X».2+1
INVERSEHYPERBOLIC SINE
ARCSINH(X)= LOG(X+ SQR(X. x + 1»
INVERSE HYPERBOLICCOSINE
ARCCOSH(X)= LOG(X+SQR(X.X -1»
INVERSE HYPERBOLICTANGENT
ARCTANH(X)= LOG« 1+ X)/(1- X»/2
INVERSE HYPERBOLICSECANT ARCSECH(X)= LOG«SQR
(-X.X+ 1)+ I/X)
INVERSE HYPERBOLICCOSECANT
ARCCSCH(X)= LOG«SGN(X). SQR
(X.X+l/x)
INVERSE HYPERBOLICCOTAN-
ARCCOTH(X)= lOG«X + 1)/(x-l »/2
GENT