Mathematical Functions¶

Built-In Mathematical Functions¶

BASIC-80 provides the following built-in mathematical functions:

Trigonometric Functions¶

SIN - Sine
COS - Cosine
TAN - Tangent
ATN - Arctangent

Exponential and Logarithmic¶

EXP - Exponential (e^x)
LOG - Natural logarithm

Other Math Functions¶

ABS - Absolute value
SQR - Square root
SGN - Sign (-1, 0, or 1)
INT - Integer part (floor)
FIX - Truncate to integer
RND - Random number

Derived Mathematical Functions¶

The following functions are NOT built-in but can be calculated using the intrinsic functions above.

Derived Trigonometric Functions¶

Function	BASIC-80 Equivalent
Secant	`SEC(X) = 1/COS(X)`
Cosecant	`CSC(X) = 1/SIN(X)`
Cotangent	`COT(X) = 1/TAN(X)`

Inverse Trigonometric Functions¶

Function	BASIC-80 Equivalent
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(XX-1)) + SGN(SGN(X)-1) 1.5708`
Inverse Cosecant	`ARCCSC(X) = ATN(X/SQR(XX-1)) + (SGN(X)-1) 1.5708`
Inverse Cotangent	`ARCCOT(X) = -ATN(X) + 1.5708`

Hyperbolic Functions¶

Direct Hyperbolic Functions¶

Function	BASIC-80 Equivalent
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 Functions¶

Function	BASIC-80 Equivalent
Inverse Hyperbolic Sine	`ARCSINH(X) = LOG(X + SQR(X*X + 1))`
Inverse Hyperbolic Cosine	`ARCCOSH(X) = LOG(X + SQR(X*X - 1))`
Inverse Hyperbolic Tangent	`ARCTANH(X) = LOG((1 + X) / (1 - 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) + 1) / X)`
Inverse Hyperbolic Cotangent	`ARCCOTH(X) = LOG((X + 1) / (X - 1)) / 2`

Example Usage¶

Computing Inverse Sine¶

10 REM Inverse sine function
20 DEF FNARCSIN(X) = ATN(X/SQR(-X*X+1))
30 INPUT "Enter value (-1 to 1)"; V
40 PRINT "ARCSIN("; V; ") = "; FNARCSIN(V)

Computing Hyperbolic Sine¶

10 REM Hyperbolic sine function
20 DEF FNSINH(X) = (EXP(X) - EXP(-X)) / 2
30 INPUT "Enter value"; V
40 PRINT "SINH("; V; ") = "; FNSINH(V)

Computing Secant¶

10 REM Secant function
20 DEF FNSEC(X) = 1 / COS(X)
30 INPUT "Enter angle in radians"; A
40 PRINT "SEC("; A; ") = "; FNSEC(A)

Constants¶

Important Mathematical Constants¶

' PI can be computed with ATN(1) * 4
' Note: ATN(1) * 4 gives single precision (~7 digits)
' For double precision, use ATN(CDBL(1)) * 4
PI = 3.1415927          ' Single-precision approximation
PI# = 3.141592653589793 ' Double-precision value

' E can be computed with EXP(1)
E = 2.7182818           ' Single-precision approximation
E# = 2.718281828459045  ' Double-precision value

Computing Pi¶

10 REM Calculate PI (single-precision)
20 PI = ATN(1) * 4
30 PRINT "PI = "; PI
40 REM For double-precision, use CDBL or # suffix
50 PI# = ATN(CDBL(1)) * 4
60 PRINT "PI# = "; PI#

Built-in Mathematical Functions¶

SIN - Sine (in radians)
COS - Cosine (in radians)
TAN - Tangent (in radians)
ATN - Arctangent (in radians)
EXP - Exponential (e^x)
LOG - Natural logarithm
SQR - Square root
ABS - Absolute value
SGN - Sign (-1, 0, or 1)

Defining Custom Functions¶

Use DEF FN to define your own mathematical functions:

10 DEF FNHYPOT(X, Y) = SQR(X*X + Y*Y)
20 PRINT "Hypotenuse of 3,4 triangle = "; FNHYPOT(3, 4)