Radio Shack TRS-80 Model III - Page 249

APPENDIX
E /
Derived
Functions
Function
Function Expressed
in Terms of
Model III
BASIC
Functions.
X is in radians.
SECANT
COSECANT
COTANGENT
INVERSE SINE
INVERSE
COSINE
INVERSE SECANT
INVERSE
COSECANT
INVERSE COTANGENT
HYPERBOLIC SINE
HYPOBOLIC
COSINE
HYPERBOLIC TANGENT
HYPERBOLIC SECANT
HYPERBOLIC COSECANT
HYPERBOLIC
COTANGENT
INVERSE HYPERBOLIC
SINE
INVERSE
HYPERBOLIC
COSINE
INVERSE HYPERBOLIC
TANGENT
INVERSE HYPERBOLIC
SECANT
INVERSE HYPERBOLIC
COSECANT
INVERSE
HYPERBOLIC
COTANGENT
SEC(X)
=
VCOS(X)
CSC(X)
=1/SIN(X)
COT(X)
=1/TAN(X)
ARCSIN(X)
=
ATN(XSQR(
X*X+1))
ARCCOS(X)
=
ATN(X SQR(
X*X i
1 ))
+
1
.5708
ARCSEC(X)
=
ATN(SQR(X*X
-
1))
-t
(SGN(X)-
1)*1.5708
ARCCSC(X)
=
ATN(1 SQR(X*X
1))
+
(SGN(X) 1
)*1
.5708
ARCCOT(X)
=
-ATN(X)
+
1.5708
SINH(X)
=
(EXP(X) "EXP(-X)).'2
COSH(X)
=
(EXP(X)
+
EXP(
X))2
TANH(X)
=
-EXP(
X)(EXP(X) + EXP( X))*2 +
1
SECH(X)
=
2/(EXP(X)
+
EXP(
X))
CSCH(X)
=
2/(EXP(X) -EXP(-X))
COTH(X)
=
EXP(-
X)/(EXP(X) EXP(
X))*2+
1
ARGSINH(X)
=
LOG(X
+
SQR(X*X+1))
ARGCOSH(X)
-
LOG(X + SQR(X*X-
1))
ARGTANH(X)
=
LOG((1
+X)/(1 -X))/2
ARGSECH(X)
=
LOG((SQR(
-
X*X+1) + 1)/X)
ARGCSCH(X)
=
LOG((SGN(X)*SQR(X*X+1)
M)X)
ARGCOTH(X)
=
LOG((X +
1)/(X-1))/2
Valid
Input
Ranges
Inverse
Sine
Inverse Cosine
Inverse Secant
Inverse
Cosecant
Inverse Hyper. Cosine
Inverse Hyper.
Tangent
Inverse
Hyper. Secant
Inverse Hyper. Cosecant
Inverse Hyper.
Cotangent
-1
<
X
<
1
-
1
<
X
<
1
X <
-
or
X>1
X
<
-
1
or
X
>
1
X
>
1
X*X
<
1
< X
<
1
X <>
X*X
>
1
Certain special
values are
mathematically
undefined,
but
our functions may
provide invalid
values:
TAN and SEC
of
90 and
270 degrees
COT and CSC
of and 180 degrees
For example,
TAN( 1.5708)
returns
a
value but TAN(90*
.01745329)
returns
a
DIVISION
BY ZERO
error.
90*
.01745329
=
1.5708
239