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Java Why is Math.sin(Math.PI/2) returning an exact value but not Math.sin(Math.PI*2)?

S

shivajikobardan

Legendary Coder
System.out.println(Math.PI); //3.141592653589793
System.out.println(Math.sin(Math.PI));//1.2246467991473532E-16

Yes sin(180d) is 0 and the above value is near to 0.

System.out.println(Math.sin(2 *

Math.PI));//-2.4492935982947064E-16

Yes sin(360d) is 0 and the above value is near to 0.

However,

Math.sin(Math.PI/2) return 1.0

Now, I don't get why this returns 1.0 and why not a number near to 1 but not exactly 1?

Math.sin(Math.PI/6) returns 0.5

Same question here because Math.PI is not exact, why is its division so exact?
 
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The reason for the results you see especially in the "corners" where sine should be zero, is due to the rounding of the float representation of PI.

This rounding goes through the calculations, which usually but not always, gets the perfect results in trigonometric functions.

I believe that there is someone on this site who can explain it better than I can, since I dont do very well with these mathematical things in English.
 
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