// mixins

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

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

@function pi() {
	@return 3.14159265359;
}

@function rad($angle) {
	$unit: unit($angle);
	$unitless: $angle / ($angle * 0 + 1);
	// If the angle has 'deg' as unit, convert to radians.
	@if $unit == deg {
		$unitless: $unitless / 180 * pi();
	}
	@return $unitless;
}

@function sin($angle) {
	$sin: 0;
	$angle: rad($angle);
	// Iterate a bunch of times.
	@for $i from 0 through 10 {
		$sin: $sin + pow(-1, $i) * pow($angle, (2 * $i + 1)) / fact(2 * $i + 1);
	}
	@return $sin;
}

@function cos($angle) {
	$cos: 0;
	$angle: rad($angle);
	// Iterate a bunch of times.
	@for $i from 0 through 10 {
		$cos: $cos + pow(-1, $i) * pow($angle, 2 * $i) / fact(2 * $i);
	}
	@return $cos;
}

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