Thread Subject: Problem with Symbolic Math

Hi Friends,
This problem is to be solved by symbolic math but the solution it gives me does not tally with what the actual solution should be:

The problem is to integrate a symbolic function of x, y, w and t with respect to x and evaluate the integrand from -pi/2 to pi/2. So the code below was written:

syms N x y w t real
A = N*cos(x-y)*cos(w*t-y);
B = int(A, x, -pi/2, pi/2);

The expected solution is:

B should equal N*sin(x-y)*cos(w*t-y) evaluated at (x=pi/2) minus same expression evaluated at (x=-pi/2). Naturally, the final solution should be:

B = N*(sin(pi/2-y) - sin(-pi/2-y))*cos(w*t-y) = 2*N*cos(y)*cos(w*t-y).

Symbolic toolbox gives me:

B = N*cos(-w*t+2*y)+N*cos(w*t)

I cannot see how this solution is correct.

Please I need this clarified so as to continue using this wonderful tool.

They are exactly the same!!!

You know the following trigonometric identity right?

cos a * cos b = 0.5*(cos(a+b) + cos(a-b))

In your case, a = y and b = wt - y.








"Good " <modeebuo@yahoo.co.uk> wrote in message <gv9t5p$qk1$1@fred.mathworks.com>...
> Hi Friends,
> This problem is to be solved by symbolic math but the solution it gives me does not tally with what the actual solution should be:
>
> The problem is to integrate a symbolic function of x, y, w and t with respect to x and evaluate the integrand from -pi/2 to pi/2. So the code below was written:
>
> syms N x y w t real
> A = N*cos(x-y)*cos(w*t-y);
> B = int(A, x, -pi/2, pi/2);
>
> The expected solution is:
>
> B should equal N*sin(x-y)*cos(w*t-y) evaluated at (x=pi/2) minus same expression evaluated at (x=-pi/2). Naturally, the final solution should be:
>
> B = N*(sin(pi/2-y) - sin(-pi/2-y))*cos(w*t-y) = 2*N*cos(y)*cos(w*t-y).
>
> Symbolic toolbox gives me:
>
> B = N*cos(-w*t+2*y)+N*cos(w*t)
>
> I cannot see how this solution is correct.
>
> Please I need this clarified so as to continue using this wonderful tool.

"Good " <modeebuo@yahoo.co.uk> wrote in message
news:gv9t5p$qk1$1@fred.mathworks.com...
> Hi Friends,
> This problem is to be solved by symbolic math but the solution it gives me
> does not tally with what the actual solution should be:
>
> The problem is to integrate a symbolic function of x, y, w and t with
> respect to x and evaluate the integrand from -pi/2 to pi/2. So the code
> below was written:
>
> syms N x y w t real
> A = N*cos(x-y)*cos(w*t-y);
> B = int(A, x, -pi/2, pi/2);
>
> The expected solution is:
>
> B should equal N*sin(x-y)*cos(w*t-y) evaluated at (x=pi/2) minus same
> expression evaluated at (x=-pi/2). Naturally, the final solution should
> be:
>
> B = N*(sin(pi/2-y) - sin(-pi/2-y))*cos(w*t-y) = 2*N*cos(y)*cos(w*t-y).
>
> Symbolic toolbox gives me:
>
> B = N*cos(-w*t+2*y)+N*cos(w*t)
>
> I cannot see how this solution is correct.
>
> Please I need this clarified so as to continue using this wonderful tool.

EDU>> syms N x y w t real
EDU>> B1 = 2*N*cos(y)*cos(w*t-y)
EDU>> B2 = N*cos(-w*t+2*y)+N*cos(w*t)

EDU>> simplify(B1-B2)

ans =

0

--Nasser