{ Derived mathematical functions. Taken from Appendix E of the AmigaBASIC Manual. Date: 27th December 1993 } '..SECANT DEF SEC(X)=1/COS(X) '..COSECANT DEF CSC(X)=1/SIN(X) '..COTANGENT DEF COT(X)=1/TAN(X) '..INVERSE SINE DEF ARCSIN(X)=ATN(X/SQR(-X*X+1)) '..INVERSE COSINE DEF ARCCOS(X)=-ATN(X/SQR(-X*X+1))+1.5708 '..INVERSE SECANT DEF ARCSEC(X)=ATN(X/SQR(X*X-1))+SGN(SGN(X)-1)*1.5708 '..INVERSE COSECANT DEF ARCCSC(X)=ATN(X/SQR(X*X-1))+(SGN(X)-1)*1.5708 '..INVERSE COTANGENT DEF ARCCOT(X)=ATN(X)+1.5708 '..HYPERBOLIC SINE DEF SINH(X)=(EXP(X)-EXP(-X))/2 '..HYPERBOLIC COSINE DEF COSH(X)=(EXP(X)+EXP(-X))/2 '..HYPERBOLIC TANGENT DEF TANH(X)=(EXP(-X)/EXP(X)+EXP(-X))*2+1 '..HYPERBOLIC SECANT DEF SECH(X)=2/(EXP(X)+EXP(-X)) '..HYPERBOLIC COSECANT DEF CSCH(X)=2/(EXP(X)-EXP(-X)) '..HYPERBOLIC COTANGENT DEF COTH(X)=EXP(-X)/(EXP(X)-EXP(-X))*2+1 '..INVERSE HYPERBOLIC SINE DEF ARCSINH(X)=LOG(X+SQR(X*X+1)) '..INVERSE HYPERBOLIC COSINE DEF ARCCOSH(X)=LOG(X+SQR(X*X-1)) '..INVERSE HYPERBOLIC TANGENT DEF ARCTANH(X)=LOG((1+X)/(1-X))/2 '..INVERSE HYPERBOLIC SECANT DEF ARCSECH(X)=LOG((SQR(-X*X+1)+1)/X) '..INVERSE HYPERBOLIC COSECANT DEF ARCCSCH(X)=LOG(SGN(X)*SQR(X*X+1)+1)/X '..INVERSE HYPERBOLIC COTANGENT DEF ARCCOTH(X)=LOG((X+1)/(X-1))/2