why simulink gives wrong answer of trigonometery

Kindly guide me when I am doing trigonometry operation by Simulink why it gives the wrong result for sin(pi), sin(2pi) and cos(pi/2)

[mahmood hassan]

Image of the my simulink simulation is attached

Answer 1

[Star Strider]

It seems that you are seeing floating-point approximation error.

See Why is 0.3 - 0.2 - 0.1 (or similar) not equal to zero? (link) for a comprehensive discussion.

[mahmood hassan]

Have you seen the image that I attached?

[mahmood hassan]

I am getting result of sin(pi) in exponential but sin(pi)=0

[Star Strider]

Yes.

They are:

[  sin(pi)       sin(2*pi)        cos(pi/2)]
122.4647e-018  -244.9294e-018    61.2323e-018

and are not equal to 0 because of floating-point approximation error that accumulates in the series calculation of the functions. This is essentially the same problem as in (1/3) = 0.3333... Multiplying that by 3 yields 0.9999..., not 1. There are extended discussions in Answers on this. I refer you to them.

[mahmood hassan]

Thanks a lot. I got your point. May you tell me any solution for this as I can get an accurate result of these?

[Star Strider]

My pleasure.

The results are accurate, or as accurate as IEEE 754 floating-point calculations permit. I am not sufficiently familiar with Simulink to know if format options are available in the output blocks. You could probably test and have the absolute values of outputs lower than perhaps 1E-17 be set to 0. The results of the calculations involving those changed values likely would not be significantly affected.

[mahmood hassan]

OK Thanks

[Star Strider]

My pleasure.