# System of nonlinear equations

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Aleem Andrew on 12 Feb 2020
Commented: David Goodmanson on 13 Feb 2020
I have tried the following code to solve a system of nonlinear equations, but it does not return the correct result which can be found on Wolfram Alpha: https://www.wolframalpha.com/input/?i=10cos15+%28%28t%2B+%282%29%2845-10sin%2815%29t%29%2F%2810sin15%2Bsqrt%2819.6*%2845-10sin%2815%29t%29%29%29%29%29+%3D+40
Can anyone suggest how I should modify the code? I want to store the value of t in another variable r that can be used for later computations.
syms t y a
%b(1) = 10*cos(15)*((t+ 2*(45-10*sin(15)*t)/(10*sin(15)+sqrt(19.62*(45-10*sin(15)*t)))))-40;
b(1) = (10*cos(15)*((t+ 2*(45-10*sin(15)*t))))*power(( 10*sin(15)+sqrt(19.62*(45-10*sin(15)*t))),-1)-40;
z = solve(b,t,y);
Xsoln = simplify(z.t);
subs(Xsoln,a)
r = a;

David Goodmanson on 12 Feb 2020
Hi Aleem,
Wolfram Alpha is solving this numercially not analytiaclly so you might as well, too.
b = @(t) 10*cosd(15)*(t+ 2*(45-10*sind(15)*t)/(10*sind(15)+sqrt(19.6*(45-10*sind(15)*t))))-40;
fzero(b,1)
ans =
1.4850
One important change here is that you have to use sind(theta) instead of sin(theta) since the angles are in degrees. Also I changed 19.62 to 19.6, otherwise the answer will disagree with Wolfram Alpha.

Aleem Andrew on 13 Feb 2020
Thank you
darova on 13 Feb 2020