ITERATIVE SOLUTION OF ONE UNKNOWN VALUE IN AN EQUATION

Please I need an iput on how to solve the value of t in the following equation x = cos(t) - y*sin(t).

%% Solution for t

x = 0.9991/1.02;

y = 2.1838/1.2544;

Answer 1

[John D'Errico]

Hint: try solving for t.

syms x y t
tsol = solve(x == cos(t) - y*sin(t),t)

tsol = 

So there are two solutions. Much of the time, a fully real solution will not exist. That will depend on the values of x and y.

subs(tsol,[x,y],[0.9991/1.02,2.1838/1.2544])

ans = 

vpa(ans)

ans = 

You can ignore the imaginary part of that, since it is essentially a VPA zero.

Alternatively, you could just use fzero.

txyfun = @(t,x,y) cos(t) - y*sin(t) - x;
x = 0.9991/1.02;
y = 2.1838/1.2544;
tfun = @(t) txyfun(t,x,y);

First, PLOT IT. Does a solution exist?

fplot(tfun)
yline(0)

So it would appear there are infinitely many solutions. fzero can find one of them. I don't even need to give it a brack around a root in this case.

[tval,fval,exitflag] = fzero(tfun,0)

tval = 0.0117

fval = 0

exitflag = 1