APPENDIX D

DERIVED MATHEMATICAL FUNCTIONS


The following functions, while not intrinsic to Standard BASIC, can be calculated using the existing BASIC functions:


Function: BASIC equivalent:
SECANT SEC(X)=1/COS(X)
COSECANT CSC(X)=1/SIN(X)
COTANGENT COT(X)=1/TAN(X)
INVERSE SINE ARCSIN(X)=ATN(X/SQR(-X*X+1))
INVERSE COSINE ARCCOS(X)=-ATN(X/SQR(-X*X+1))+1.5708
INVERSE SECANT ARCSEC(X)=ATN(X/SQR(X*X-1))+SGN(SGN(X)-l)*1.5708
INVERSE COSECANT ARCCSC(X)=ATN(X/SQR(X*X-1))+(SGN(X)-1)*1.5708
INVERSE COTANGENT ARCCOT(X)=ATN(X)+1.5708
HYPERBOLIC SINE SINH(X)=(EXP(X)-EXP(-X))/2
HYPERBOLIC COSINE COSH(X)=(EXP(X)+EXP(-X))/2
HYPERBOLIC TANGENT TANH(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
INVERSE HYPERBOLIC SINE ARCSINH(X)=LOG(X+SQR(X*X+1))
VERSE HYPERBOLIC COSINE ARCCOSH(X)=LOG(X+SQR(X*X-1))
INVERSE HYPERBOLIC TANGENT ARCTANH(X)=LOG((l+X)/(l-X))/2
INVERSE HYPERBOLIC SECANT ARCSECH(X)=LOG((SQR(-X*X+1)+1)/X)
INVERSE HYPERBOLIC COSECANT ARCCSCH(X)=LOG((SGN(X)*SQR(X*X+1)+l)/X)
INVERSE HYPERBOLIC COTANGENT ARCCOTH(X)=LOG((X+l)/(X-1))/2

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