added sine.js and sine_radians.js

sine.js

@@ -0,0 +1,14 @@
+const sine_radians = require("./sine_radians.js");
+
+/**
+ * @param {String} n - radians
+ * @returns {String} sine of n
+ */
+function sine() {
+  const n = arguments[0];
+  const options = arguments[1];
+  return sine_radians(n, options);
+}
+
+module.exports = sine;
+module.exports.default = sine;

sine_radians.js

@@ -0,0 +1,38 @@
+"use strict";
+
+const add = require("./add.js");
+const is_zero = require("./is_zero.js");
+const square = require("./square.js");
+const multiply_rational = require("./multiply_rational.js");
+const divide = require("./divide.js");
+
+function sine_radians(n, { steps = 100, max_decimal_digits = 100 } = {}) {
+  if (is_zero(n)) return "0";
+
+  let sign = "-";
+  let result = n;
+  let imax = steps;
+  let nsquare = square(n);
+  let numerator = n;
+  let denominator = "1";
+  let f1;
+  let f2 = "1";
+  for (let i = 0; i < imax; i++) {
+    f1 = add(f2, "1");
+    f2 = add(f1, "1");
+
+    // same as increasing the power by 2
+    numerator = multiply_rational([numerator, nsquare], { max_decimal_digits });
+    denominator = multiply_rational([denominator, f1, f2], { max_decimal_digits });
+    const diff = divide(numerator, denominator, { max_decimal_digits });
+    // console.log({ f1, f2, sign, numerator, denominator, diff });
+
+    result = add(result, sign + diff);
+
+    sign = sign === "-" ? "+" : "-";
+  }
+  return result;
+}
+
+module.exports = sine_radians;
+module.exports.default = sine_radians;