tan() in Java returning a strange value

Question

My code passes an angle in radians to the cos, tan and sin. Everything seems to work fine except tan of 90, which gives the value 16331239353195370 for some odd reason. Example code:

import java.text.DecimalFormat;

public class mathtable {

  public static void main(String[] args) {

    System.out.println("Angle   Sin Cos Tan");
    System.out.println("-----   --- --- ---");

    for (double angle = 0.0; angle < 180; angle +=5) {
      double angle_rad = Math.toRadians(angle);
      double sin = Math.sin(angle_rad);
      String sin_4 = new DecimalFormat("#.####").format(sin);
      double cos = Math.cos(angle_rad);
      String cos_4 = new DecimalFormat("#.####").format(cos);
      double tan = Math.tan(angle_rad);
      String tan_4 = new DecimalFormat("#.####").format(tan);
      System.out.println(angle + "  " + sin_4 + "   " + cos_4 + "   " + tan_4);
    }
  }
}

Why is the value returned not strictly equal to IEEE infinity?

Answer 1

Well, tan(pi/2) in radians is essentially infinite, isn't it? So you'd expect to get a very large number, wouldn't you? (It's not infinity because pi/2 can't be exactly represented as a double. You're finding a value on an asymptotic curve very close to where it would become infinite.)

See these graphs of sin/cos/tan to see what I mean, remembering that pi/2 radians is 90 degrees.