mathjs/lib/function/trigonometry/csc.js

module.exports = function (math) {
  var util = require('../../util/index.js'),

      Complex = require('../../type/Complex.js'),
      Unit = require('../../type/Unit.js'),
      collection = require('../../type/collection.js'),

      isNumBool = util.number.isNumBool,
      isComplex = Complex.isComplex,
      isUnit = Unit.isUnit,
      isCollection = collection.isCollection;

  /**
   * Calculate the cosecant of a value, csc(x) = 1/sin(x)
   *
   *     csc(x)
   *
   * For matrices, the function is evaluated element wise.
   *
   * @param {Number | Boolean | Complex | Unit | Array | Matrix} x
   * @return {Number | Complex | Array | Matrix} res
   */
  math.csc = function csc(x) {
    if (arguments.length != 1) {
      throw new util.error.ArgumentsError('csc', arguments.length, 1);
    }

    if (isNumBool(x)) {
      return 1 / Math.sin(x);
    }

    if (isComplex(x)) {
      // csc(z) = 1/sin(z) = (2i) / (exp(iz) - exp(-iz))
      var den = 0.25 * (Math.exp(-2.0 * x.im) + Math.exp(2.0 * x.im)) -
          0.5 * Math.cos(2.0 * x.re);

      return new Complex (
          0.5 * Math.sin(x.re) * (Math.exp(-x.im) + Math.exp(x.im)) / den,
          0.5 * Math.cos(x.re) * (Math.exp(-x.im) - Math.exp(x.im)) / den
      );
    }

    if (isUnit(x)) {
      if (!x.hasBase(Unit.BASE_UNITS.ANGLE)) {
        throw new TypeError ('Unit in function csc is no angle');
      }
      return 1 / Math.sin(x.value);
    }

    if (isCollection(x)) {
      return collection.deepMap(x, csc);
    }

    if (x.valueOf() !== x) {
      // fallback on the objects primitive value
      return csc(x.valueOf());
    }

    throw new util.error.UnsupportedTypeError('csc', x);
  };
};