Cos function with Array

Hi, I am using cos function to calculate the cosine of an array as following:

a = th4_s1(2);        %second element of my "th4_s1" array, which equals 1.5708
b = cos(a);             %Matlab gives answer as 6.123e-17
c = 1.5708;
d = cos(1.5708);    %Matlab gives answer as -3.6732e-6

Why are they so different? How can I avoid this error?

Thank you.

[Stephen23]

https://web.archive.org/web/20201025055604/https://www.mathworks.com/matlabcentral/answers/625273-cos-function-with-array

Answer 1

[Walter Roberson]

>> acos(6.123e-17)
ans =
           1.5707963267949

>> acos(-3.6732e-6)
ans =
           1.5707999999949
           
>> cos(1.5708)
ans =
     -3.67320510334657e-06
     
>> acos(cos(1.5708))
ans =
                    1.5708

>> acos(cos(1.5708)) - 1.5708
ans =
     0

In other words, your th4_s1(2) is not 1.5708: it only rounds to that for display purposes, and is closer to 1.50796 .

And that cos(1.5708) is not 6.123e-17 like you show: that value is cos(1.5707999999949) not cos(1.5708) .

My recommendation would be that you go into Preferences -> Command Window -> Text Display, and choose numeric display "long g", and also Preferences -> Variables -> Default array format: and select "long g" (this affects the Variable Browser)

[Nhan Nguyen]

Thank you so much.