Apple II User Manual

                Note that (B-A)*RND(1)+A will

                generate a random number between

                A and B.

STATEMENT       SYNTAX/FUNCTION                                         EXAMPLE

SGN             SGN (expression)                                        230 PRINT SGN(X)

                Gives 1.  If X>0, 0 if X=0, and -1 if

                X<0.

STATEMENT       SYNTAX/FUNCTION                                         EXAMPLE

SIN             SIN (expression)                                        190 PRINT SIN(X)

                Gives the sine of the expression X.  X is

                interpreted as being in radians.  Note:

                COS(X) =SIN(X+3.14159/2) and that

                1 Radian = 180/PI degrees = 57.2958

                degrees; so that the sine of X degrees=

                SIN(X/57.2958).

STATEMENT       SYNTAX/FUNCTION                                         EXAMPLE

SQR             SQR (expression)                                        180 PRINT SQR(X)

                Gives the square root of the expression X.

                An FC error will occur if X is less than zero,

STATEMENT       SYNTAX/FUNCTION                                         EXAMPLE

TAN             TAN (expression)                                        200 PRINT TAN(X)

                Gives the tangent of the expression X.  X is

                interpreted as being in radians.

DERIVED FUNCTIONS

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

functions:

FUNCTION                 FUNCTION EXPRESSED IN TERMS OF BASIC FUNCTIONS

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(SQR(X*X-1))+(SGN(X)-1)*1.5708

INVERSE COSECANT*        ARCCSC(X) = ATN(1/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

*These functions require the user-defined ATN function.  See Appendix H for details.