Unexpected answer returned by Math.sin

[Porlus]

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?

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

Thanks

[Riven]

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

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

Because:

1	Math.PI != pi

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

1   2   3

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)));

[Porlus]

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

Games published by our own members! Check 'em out!

[Riven]

Is it really a problem?

[Porlus]

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

[Riven]

Note the 'e-16'

1.2246467991473532E-16
equals
0.00000000000000012246467991473532

[Porlus]

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

[Agro]

Type cast it to an integer.

[Porlus]

That's great. Thanks for the help.

[Sparky83]

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:

1   2   3

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?

Games published by our own members! Check 'em out!

[Agro]

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

[vbrain]

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:

1   2   3

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?

In NO case would typecasting to an integer be better.

[Alan_W]

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

E.g.

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

[Roquen]

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.