TAN
BASIC keyword | |
Keyword: | TAN |
Abbreviation: | – |
Type: | Function |
Token code: | 192/$C0 |
Handling routine in BASIC ROM: |
58036–58079 $E2B4–E2DF |
List of all BASIC keywords |
Remark: This article describes the BASIC-Command TAN in BASIC V2 at the Commodore 64.
Type: Numeric Function |
The numerical function TAN is a mathematical function which evaluates to the tangent for a given angle, a number regarded as being in radians.
If the term given in the parentheses is non-numerical, the BASIC error ?TYPE MISMATCH ERROR occurs. Being a floating point argument, the term must be in the range of ±2.93873588·10^{−38} to ±1.70141183·10^{38}. Exceeding these limits yields the BASIC error ?OVERFLOW ERROR. Special values like +/-π/2 (+/- 90 degree) according to the definition of the function lead to the BASIC error ?DIVISION BY ZERO. Omitting the numeric argument or to many arguments results in a ?SYNTAX ERROR.
Accuracy[edit]
The graph to the right was obtained by comparing results from the BASIC TAN function to values computed on a modern x86-type PC.
For most inputs, TAN is accurate to about 29 bits. Values for which SIN and COS lose accuracy also lose accuracy for TAN. The accuracy close to X = 0 could be improved by patching SIN to return SIN(X) = X for |X| less than 2^{-11}.
TAN calls SIN and COS, which call POLY1, which calls MLTPLY ($BA59), and consequently the multiply bug affects its results. A small number of input values give results that match to only 25 bits.
Implementation details[edit]
TAN(X) is implemented simply as SIN(X)/COS(X).
Examples[edit]
PRINT TAN(1)
Output: 1.55740772
10 DEF FN CT(X) = 1/TAN(X) 20 PRINT FN CT(45*π/180)
Defines the function of cotangent (tangent complement) as user defined function FN CT(), called with an angle of 45°.
PRINT TAN(π/2)
Provokes the error ?DIVISION BY ZERO ERROR for an argument representing the angle of 90°.
PRINT TAN(π)
On screen the value -7.3145904E-10 will be shown, a very small value near to 0 (also for all multiples of π), but not exactly reached caused by the inaccuratness of the internal implementation of the function.
ABS | AND | ASC | ATN | CHR$ | CLOSE | CLR | CMD | CONT | COS | DATA | DEF | DIM | END | EXP | FN | FOR | FRE | GET | GET# | GOSUB | GOTO | IF | INPUT | INPUT# | INT | LEFT$ | LEN | LET | LIST | LOAD | LOG | MID$ | NEW | NEXT | NOT | ON | OPEN | OR | PEEK | π | POKE | POS | PRINT | PRINT# | READ | REM | RESTORE | RETURN | RIGHT$ | RND | RUN | SAVE | SGN | SIN | SPC | SQR | STATUS/ST | STEP | STOP | STR$ | SYS | TAB | TAN | THEN | TIME/TI | TIME$/TI$ | TO | USR | VAL | VERIFY | WAIT