How would I sum a function and use fzero?

I want a function to look like this y=sin(t1-T)+sin(t2-T)+sin(t3-T)+...+sin(tn-T) and use the fzero to find T. How would I go about this? Thank you in advance.

Answer 1

[Roger Stafford]

Using ‘fzero’ on that particular problem is needlessly inefficient. You can use ‘atan2’ and ‘asin’ instead.

cn = cos(t1)+cos(t2)+...+cos(tn);
sn = sin(t1)+sin(t2)+...+sin(tn);
p = atan2(sn,cn);
as = asin(y/sqrt(sn^2+cn^2));
T1 = p-as;  % One solution (in radians)
T2 = p+as-pi;  % Another solution (in radians)

Also any multiple of 2*pi added or subtracted from T1 or T2 is a solution. (Note that the inequality y^2<=sn^2+cn^2 must be true for a solution to exist.)

[Andrei Bobrov]

+1

Answer 2

[Birdman]

t=0:0.1:10;syms T y(T);
for i=1:1:length(t)
    yy(i)=sin(t(i)-T);
end
y=symfun(sum(yy),T);
fzero(y,0.5)

Hope this helps.

[J. Nash]

Many thanks this was a great help. I couldn't get my head around it.

[Birdman]

Can you accept the answer so that other people having the same problem will know that there is a working solution?

Answer 3

[Andrei Bobrov]

f = @(T)sum(sin(t(:) - T))
fzero(f,.5)

[J. Nash]

Wow this is even shorter. Helps a lot since I have around 1000 lines of code. Many thanks for making my code easier.