SCSS/SASS module calculating sin/cos/tan using Taylor Expansion.

trig.scss

///////////////////////////////////////////////////////////////////////////////////
// Plain SASS Trigonometry Algorithm in Taylor Expansion                         //
//                                                                               //
// Based on                                                                      //
//      http://japborst.net/posts/sass-sines-and-cosines                         //
// +    http://thesassway.com/advanced/inverse-trigonometric-functions-with-sass //
///////////////////////////////////////////////////////////////////////////////////

$pi: 3.14159265359;
$_precision: 10;

@function pow($base, $exp) {
  $value: $base;
  @if $exp > 1 {
    @for $i from 2 through $exp {
      $value: $value * $base;
    }
  }
  @if $exp < 1{
    @for $i from 0 through -$exp {
      $value: $value / $base;
    }
  }
  @return $value;
}

@function fact($num) {
  $fact: 1;
  @if $num > 0{
    @for $i from 1 through $num {
      $fact: $fact * $i;
    }
  }
  @return $fact;
}

@function _to_unitless_rad($angle) {
  @if unit($angle) == "deg" {
    $angle: $angle / 180deg * $pi;
  }
  @if unit($angle) == "rad" {
    $angle: $angle / 1rad;
  }
  @return $angle;
}

@function sin($angle){
  $a: _to_unitless_rad($angle);
  $sin: $a;
  @for $n from 1 through $_precision {
    $sin: $sin + (pow(-1, $n) / fact(2 * $n + 1) ) * pow($a, (2 * $n + 1));
  }
  @return $sin;
}

@function cos($angle){
  $a: _to_unitless_rad($angle);
  $cos: 1;
  @for $n from 1 through $_precision {
    $cos: $cos + ( pow(-1,$n) / fact(2*$n) ) * pow($a,2*$n);
  }
  @return $cos;
}

@function tan($angle){
  @return sin($angle) / cos($angle);
}

$default-threshold: pi()/180/20;

@function convert-angle($value, $unit-name) {
  $factors: (
    rad: 1rad,
    deg: 180deg/pi(),
    grad: 200grad/pi(),
    turn: .5turn/pi()
  );

  @if not unitless($value) {
    @warn '`#{$value}` should be unitless';
    @return false;
  }

  @if not map-has-key($factors, $unit-name) {
    @warn 'unit `#{$unit-name}` is not a valid unit - please make sure it is either `deg`, `rad`, `grad` or `turn`';
    @return false;
  }

  @return $value*map-get($factors, $unit-name);
}

@function asin($z, $unit-name: deg, $threshold: $default-threshold) {
  $sum: 0;
  $complement: false;
  $sign: if($z != 0, $z/abs($z), 1);
  $z: abs($z);
  
  @if $z > 1 {
    @warn 'illegal `#{$z}` value for function';
    @return false;
  }

  @if $z > sin(pi()/4) {
    $complement: true;
    $z: sqrt(1 - pow($z, 2));
  }

  $term: $z;
  $i: 0;
  $k: 1;

  @while $term > $threshold {
    $sum: $sum + $term;

    $i: $i + 1;
    $k: $k*(2*$i - 1)/(2*$i);
    $j: 2*$i + 1;

    $term: $k*pow($z, $j)/$j;
  }

  @return convert-angle($sign*(if($complement, pi()/2 - $sum, $sum)), $unit-name);
}

@function acos($z, $unit-name: deg, $threshold: $default-threshold) {
  @return convert-angle(pi()/2, $unit-name) - asin($z, $unit-name, $threshold);
}

@function atan($z, $unit-name: deg, $threshold: $default-threshold) {  
  @return asin($z/sqrt(1 + pow($z, 2)), $unit-name, $threshold);
}