Unexpected answer returned by Math.sin

Newbie & Debugging Questions
#1

Hi all, I’m just wondering why the following isn’t producing the answer 0 as a sine wave normally be at when it reaches 180 degrees. Can anyone see why?

System.out.println(Math.sin(Math.toRadians(180.0)));

Thanks

#2

Math.toRadians(180.0) returns PI. PI cannot be accurately described in any base (except products of pi).


	Math.sin(Math.toRadians(180.0)) == Math.sin(Math.PI) != 0.00;

Because:


        Math.PI != pi

We can verify that Math.PI is indeed the best approximation of PI:


			System.out.println(Math.sin(Math.PI - Math.ulp(Math.PI)));
			System.out.println(Math.sin(Math.PI));
			System.out.println(Math.sin(Math.PI + Math.ulp(Math.PI)));
#3

Thanks for the reply! Ah ok, I see. Is there any way around this problem?

#4

Is it really a problem?

#5

Well the code snippet above seems to return 1.2246467991473532E-16 rather than 0. Is that typically an acceptable margin of error?

#6

Note the ‘e-16’

1.2246467991473532E-16
equals
0.00000000000000012246467991473532

#7

Ah, that’s fine then. :slight_smile: Is there an easy way to convert that to that readable format in Java? Just for testing

#8

Type cast it to an integer.

#9

That’s great. Thanks for the help. :slight_smile:

#10

I wouldn’t do typecasting to an integer, because the result will be 0 in most of the cases and will only be non zero if the angle is exactly pi/2 or 3*pi/2.

I would rather set a threshold. Like this:

double a = Math.sin(Math.toRadians(angle));
if(a < 0.0001 && a > -0.00001)
    a = 0;

In which case would typecasting to integer be better?

#11

Well, I would convert to degrees if you want to display it.

#12

In NO case would typecasting to an integer be better.

#13

You could round off the result to however many decimal places you desire.

E.g.

double result = (int)(1.0e6*sin(angle))/1.0e6
#14

KEEP IT SIMPLE

System.out.printf("%f\n", Math.sin(Math.toRadians(180.0)));

outputs: 0.000000

If you only want to see the high significant digits, use printf with %f instead of println.