title: Java Math.toRadians(angle) vs hard-calculated
body: <p>This question is related to another stackoverflow discussion <a href="https://stackoverflow.com/questions/3694380/calculating-distance-between-two-points-using-latitude-longitude-what-am-i-doi">distance between long&amp;lat points</a></p>
  
  <p>Here is the code from the top voted answer:</p>
  
  <pre><code>/*
   * Calculate distance between two points in latitude and longitude taking
   * into account height difference. If you are not interested in height
   * difference pass 0.0. Uses Haversine method as its base.
   * 
   * lat1, lon1 Start point lat2, lon2 End point el1 Start altitude in meters
   * el2 End altitude in meters
   */
  private double distance(double lat1, double lat2, double lon1, double lon2,
          double el1, double el2) {
  
      final int R = 6371; // Radius of the earth
  
      Double latDistance = deg2rad(lat2 - lat1);
      Double lonDistance = deg2rad(lon2 - lon1);
      Double a = Math.sin(latDistance / 2) * Math.sin(latDistance / 2)
              + Math.cos(deg2rad(lat1)) * Math.cos(deg2rad(lat2))
              * Math.sin(lonDistance / 2) * Math.sin(lonDistance / 2);
      Double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
      double distance = R * c * 1000; // convert to meters
  
      double height = el1 - el2;
      distance = Math.pow(distance, 2) + Math.pow(height, 2);
      return Math.sqrt(distance);
  }
  
  private double deg2rad(double deg) {
      return (deg * Math.PI / 180.0);
  }
  </code></pre>
  
  <p>The top voted answer has the following comment:</p>
  
  <p>"Why not Math.toRadians() instead of deg2rad()? It would be really self-containing."</p>
  
  <p>I looked up the Math.toRadians() method in the <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Math.html#toRadians(double)" rel="nofollow noreferrer">documentation</a> and noticed this: </p>
  
  <p>"Converts an angle measured in degrees to an approximately equivalent angle measured in radians. <strong>The conversion from degrees to radians is generally inexact.</strong>"</p>
  
  <ol>
  <li>Is the top voted answer's deg2rad method more or less exact than the Math.toRadians() method?</li>
  <li>Using the deg2rad method performs two arithmetic operations and one Math.Pi look up, its not clear how Math.toRadians() performs the convention. Assuming that this distance calculation may be performed frequently and quick response to user input is desired, which conversion method would scale more efficiently?</li>
  </ol>
  
  <p>If the answer to question 1 is that the two methods have roughly the same inexactness/accuracy, I think that I would use Math.toRadians. Using Math.ToRadians makes the code more readable, and I assume that it would scale more efficiently as well.  </p>