Why are sine and cosine values inaccurate?

Hi, I'm a medical researcher interested in DSP, and am trying to learn how to use MATLAB. I am just testing out basic functions, including sine and cosine functions. After inputting cos(pi/2) I got 6.1232e-17, and for sin(pi) I got 1.2246e-16. Clearly these are very close to the value 0 which I expected. But I am confused as to why it did not return zero. Is this round-off error?

thanks

Jem

Answer 1

[Honglei Chen]

Those are floating point errors. If you want exact zeros, you can use sind/cosd, although they are slower

sind(180)
cosd(90)

[Jem]

Many thanks Honglei, that's great.

[Gary Groves]

Hi, so where do I find information on the "d" operator that you added to the end of sin, and cos? I have been looking everywhere and the only place that I am seeing it used is here in your example. Do you have a link to a help page that explains the use of the "d" function that you used here?

[James Tursa]

https://www.mathworks.com/help/matlab/ref/sind.html?searchHighlight=sind&s_tid=srchtitle

https://www.mathworks.com/help/matlab/ref/cosd.html?searchHighlight=cosd&s_tid=srchtitle

[John D'Errico]

d is not an "operator". sind and cosd are simply other functions that have been defined in MATLAB for the use of people who prefer to work/think in terms of degrees and not radians. Other functions, such as tand, atand, etc., are also defined to work in the same way.

[Steven Lord]

In addition, if you are computing the sine and cosine of multiples of π (the pi function returns a value very close to, but not exactly equal to, the value of the irrational number π) you could use the sinpi and cospi functions or you could perform the calculations symbolically using Symbolic Math Toolbox.

radian = sin(pi)

radian = 1.2246e-16

degree = sind(180)

degree = 0

multipleOfPi = sinpi(1)

multipleOfPi = 0

symbolic = sin(sym(pi))

symbolic = 

0

Answer 2

[Shashank Prasanna]

pi itself is an approximation. I would point you to this solutions page for some more insight to this behavior:

http://www.mathworks.com/support/solutions/en/data/1-16FOQ/

[Jem]

Thanks Shashank. That's very useful.