i am trying to find coefficients a0 , an and bn but the output for bn seems wrong and will not simplify

i am trying to find coefficients a0 , an and bn but the output for bn seems wrong and will not simplify

i have tried using pretty, symplify, ignoreanalyticconstraint,true and simplifyFraction, but none have worked

f(x) = -3, -pi < x < 0

f(x) = 3, 0 < x < pi

syms t n
T = 2*pi
w0 = 2*pi/T
n=1:5

a0 = (1/T)*int(3,t,-pi,0) + (1/T)*int(-3,t,0,pi)

an = (2/T)*int(-3*cos(n*w0*t),t,-pi,0) + (2/T)*int(3*cos(n*w0*t),t,0,pi) 

bn = (2/T)*int(-3*sin(n*w0*t),t,-pi,0) + (2/T)*int(3*sin(n*w0*t),t,0,pi); 

pretty(bn)

[VBBV]

@scott lamb you can do double & vpa for the bn coefficient to simplify

syms t n
T = 2*pi;
w0 = 2*pi/T;
n=1:5;

a0 = (1/T)*int(3,t,-pi,0) + (1/T)*int(-3,t,0,pi);

an = (2/T)*int(-3*cos(n*w0*t),t,-pi,0) + (2/T)*int(3*cos(n*w0*t),t,0,pi); 

bn = (2/T)*int(-3*sin(n*w0*t),t,-pi,0) + (2/T)*int(3*sin(n*w0*t),t,0,pi); 
% double and vpa 
double(vpa(bn))

ans = 1x5

3.8197 0 1.2732 0 0.7639

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Answer 1

[Matt J]

Well, here is what I get for bn,

>> bn
 
bn =
 
[ 17202483417667977/4503599627370496, 0, 5734161139222659/4503599627370496, 0, 17202483417667977/22517998136852480]

You haven't told us whether you get the same thing, or if so what you would expect instead, but these terms do look nice when multiplied by pi,

>> double(bn*pi)

ans =

   12.0000         0    4.0000         0    2.4000

[Walter Roberson]

syms t n
Pi = sym(pi);
T = 2*Pi;
w0 = 2*Pi/T;
n=1:5

n = 1×5

1 2 3 4 5

a0 = (1/T)*int(3,t,-Pi,0) + (1/T)*int(-3,t,0,Pi)

a0 = 

0

an = (2/T)*int(-3*cos(n*w0*t),t,-Pi,0) + (2/T)*int(3*cos(n*w0*t),t,0,Pi) 

an = 

bn = (2/T)*int(-3*sin(n*w0*t),t,-Pi,0) + (2/T)*int(3*sin(n*w0*t),t,0,Pi); 

pretty(bn)

/ 12      4      12  \
| --, 0, --, 0, ---- |
\ pi     pi     5 pi /

[Matt J]

scott lamb's comment moved here:

thank you it pi=sym(pi) , i was missing