Why did I get different results by using degree/radiance as the unit in the integration?

today I wonder if the unit (degree/radiance) of integration variable matters in Matlab, so I tried these 2 peices of codes:

x_tst=0:0.1:180; % in degree
y_tst=sind(x_tst);
Q1=trapz(x_tst,y_tst)

Q1 =

     1.145915299373423e+02 

x_tst_deg=0:0.1:180; 
x_tst_rad=x_tst_deg./180.*pi;% in radiance 
y_tst=sin(x_tst_rad);
Q2=trapz(x_tst_rad,y_tst)

Q2 =

   1.999949230172279

As you can see, the results are different, could someone tell me why we have this problem in MATLAB?

Must we use radiance as the unit of angle in Matlab (especially in the integration)?

What if I would like to adopt 'degree' as the unit of the integration variable?

Answer 1

[KSSV]

Note that both the results are same...but they are in different units....

Your Q1 is in degrees and Q2 is in radians.....Convert them to the same units and see...

% Check  in degrees
Q2*180/pi 
Q1
% check in radians 
Q1*pi/180
Q2

[Shuangfeng Jiang]

Thx for answering.

If we calculate the integration by hand (either in degree or in radiance), the result is 2, which is close to Q2. However, Q1 deviates from 2. Does it mean MATLAB tacitly assume the unit of the integration variable is radiance?

[KSSV]

It depends on you......if angle in radians use sin, if angles in degrees use sind. So it depends on what you are using sin or Sind.

[Shuangfeng Jiang]

Can you please explain why Q1 deviates from the correct result(2)?

[KSSV]

Simple man...your x-values i.e x_tst are in radians for Q1 and are in degrees for Q2...as the area is length*breadth...your x-values are different in both the cases...so your values are different.