Hi!! What is wrong in my code?

 syms x y t
 0<=t & t<=1;
 eqns = [x^2 + y^2 -1 == 0, x - t*cos(0)==0, y - t*sin(0)==0];
 vars = [x y];
 [solv, solu] = solve(eqns, vars)

This is what I get:

solv =

Empty sym: 0-by-1

solu =

Empty sym: 0-by-1

With that code, I want to know the point of intersection between the circumference and the segment line. I hope someone can help me.

[Rik]

In addition to what Star Strider and Walter commented, are you sure you mean assume(0<=t&t<=1) and not assume(0 >=t&t<=1)? Because the former is equivalent to assume(t<=1) and allows the solution [x,y,t]=[-1,0,-1] as well.

[John Medina]

The segment line goes from (0,0) to (1,0) with direction (1,0) equivalent to angle = 0 (radian). So, t (the parameter) must go from 0 to 1. Forgive for my grammar.

[Rik]

Then you should indeed use assume(0 >=t&t<=1).

Answer 1

[Star Strider]

First, MATLAB parses matrices differently than you would expect it to, so your original ‘eqns’ system is (as MATLAB reads it) is:

eqns =
[ x^2 + y^2, 0, x - t == 0, y == 0]

Second, you need to be a bit less restrictive with respect to what you request of solve:

syms x y t
assume(0<=t & t<=1)
eqns = [x^2+y^2-1==0, x-t*cos(0)==0, y-t*sin(0)==0];
s = solve(eqns)
ts = s.t
xs = s.x
ys = s.y

ts =
1

xs =
1

ys =
0

It cannot solve for both ‘x’ and ‘y’ simultaneously in the system you posted.

[John Medina]

Thanks!

[Star Strider]

My pleasure!

Answer 2

[Walter Roberson]

 syms x y t
 assume(0<=t & t<=1);
 eqns = [x^2 + y^2 - 1 == 0, x - t*cos(0)==0, y - t*sin(0)==0];  %notice spacing change
 vars = [x y];
 sol = solve(eqns);
 sol2 = subs(vars, sol);
 solv = sol2(:,1);
 solu = sol2(:,2);

[John Medina]

Thanks!