bcSind(...) - PHP Science Labs

PHPSL Function: bcSind( )

bcSind ($AngDeg)

Dependencies: NONE

This function computes the circular sine to up to 100 decimals for angular arguments in degrees rather than in radians.

The decimals argument can range from $1$ to $100$, with default decimals = $16$.

The circular sine value is computed from the series derived from Taylor's theorem, where $(x)$ is the angle expressed in natural radians:

$ \begin{align*} x ~=~ \frac{degrees \cdot \pi}{180} ~ radians \end{align*} $

$ \begin{align*} sin(x) = \sum^\infty_{n=0} \frac{(-1)^n \cdot {x}^{2n+1}}{(2n+1)!} = \frac{x^1}{1!} ~-~ \frac{x^3}{3!} ~+~ \frac{x^5}{5!} ~~-~~ \frac{x^7}{7!} ~+~ \frac{x^9}{9!} ~-~ \cdot \cdot~\cdot \end{align*} $

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/* __________________________________________________ This function computes the circular sine to up to 100 decimals precision for an angle argument given in decimal degrees. Author : Jay Tanner - 2024 License : Public Domain __________________________________________________ */ function bcSind ($AngDeg, $Decimals=16) { // ____________________________________________ // Read angular argument in degrees. It should // be in the form of a numeric string, such // as '12.345', so as not to be confused // with a normal double-precision value. $a = trim($AngDeg); // __________________________________________ // Set decimals precision, not to exceed 100. $decimals = floor(abs($Decimals)); if ($decimals > 100) {$decimals = 100;} if ($decimals < 1) {$decimals = 1;} $d = abs(intval($decimals)) + 8; // ______________________________________________________ // Reasonably handle negative and excessive angle values. while(bccomp($a, '0', $d) < 0) {$a = bcadd($a, '360', $d);} while(bccomp($a, '360', $d) > 0) {$a = bcsub($a, '360', $d);} // ___________________________________________________________ // Define internal constant for degrees-to-radians conversion. // This local constant could also be made global. $RAD_PER_DEG = '0.01745329251994329576923690768488612713442871888541725456097191440171009114603449443682241569634509482212304492'; $x = bcmul($a, $RAD_PER_DEG, $d); // ___________________________________________________________________ // Remove, but remember the numerical sign to be reattached to result. $NumSign = '+'; if (bccomp($x, '0', $decimals) < 0) {$x = str_replace('-', '', $x); $NumSign = '-';} // ______________________________________ // Compute sine value from Taylor series. $PrecisionLimit = '0.' . str_repeat('0', $decimals) . '1'; $term = $n = $denom = 1; $nps = -1; $sinx = $x; while (abs($term) > $PrecisionLimit) { $numer = bcmul($nps, bcpow($x, 2*$n+1, $d), $d); $denom = bcmul(bcmul($denom, 2*$n), 2*$n+1); $term = bcdiv($numer, $denom, $d); $sinx = bcadd($sinx, $term, $d); $nps = -$nps; $n++; } // _____________________________________________________ // Round-off sine value to specified number of decimals. $Z = '0.' . str_repeat('0', $decimals) . '5'; $w = $NumSign.bcadd($sinx, $Z, $decimals); // _____________________________ // Patch to fix +- sign anomaly. $sinx = str_replace('+-', '-', $w); return $sinx; } // END OF bcSind(...)
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EXAMPLE call results:
```
   print bcSind('60', 32);
// =--> 0.86602540378443864676372317075293


   print bcSind('-22.35173', 40);
// =--> -0.3802913385144120452500631279440739354945
```
Reference(s):

https://en.wikipedia.org/wiki/Taylor_series

Jay Tanner - 2024