why am i getting ans = Empty sym: 0-by-1

clc

%variables
 syms X Y;
solve  (cos(X+0.5)+Y==0.8,X)
solve  (sin(Y)-2*X==1.6,Y)

%convergence

G1(Y)=-acos(4/5 - Y) - 1/2;
G2(X)=pi - asin(2*X + 8/5);

%Derivative

G1X=diff(G1,X)
G1Y=diff(G1,Y)
G2X=diff(G2,X)
G2Y=diff(G2,Y)

%convergence limits

solve(-2/(1 - (2*X + 8/5)^2)^(1/2)==1)
solve(-2/(1 - (2*X + 8/5)^2)^(1/2)==-1)

solve(-1/(1 - (Y - 4/5)^2)^(1/2)==1)
solve(-1/(1 - (Y - 4/5)^2)^(1/2)==-1)

after convergence limits i am getting ans = Empty sym: 0-by-1, why is this and how to fix it

ans =
 
Empty sym: 0-by-1
 
 
ans =
 
 - (3^(1/2)*1i)/2 - 4/5
   (3^(1/2)*1i)/2 - 4/5
 
 
ans =
 
Empty sym: 0-by-1
 
 
ans =
 
4/5

Answer 1

[Star Strider]

‘There’s no “there” there!’

When in doubt, plot! The plot of a funciton tells essentially everything that needs to be known about its behaviour.

The first and third functions never reach +1 so there is no solution to either of them.

%variables
syms X Y;
solve  (cos(X+0.5)+Y==0.8,X)

ans = 

solve  (sin(Y)-2*X==1.6,Y)

ans = 

%convergence

G1(Y)=-acos(4/5 - Y) - 1/2;
G2(X)=pi - asin(2*X + 8/5);

%Derivative

G1X=diff(G1,X)

G1X(Y) = 

0

G1Y=diff(G1,Y)

G1Y(Y) = 

G2X=diff(G2,X)

G2X(X) = 

G2Y=diff(G2,Y)

G2Y(X) = 

0

%convergence limits
eq1 = -2/(1 - (2*X + 8/5)^2)^(1/2)-1

eq1 = 

figure
fplot(eq1,[-2 0])
grid
ylim([-25, 5])

solve(-2/(1 - (2*X + 8/5)^2)^(1/2)==1, X)

 
ans =
 
Empty sym: 0-by-1
 

solve(-2/(1 - (2*X + 8/5)^2)^(1/2)==-1)

ans = 

eq2 = -1/(1 - (Y - 4/5)^2)^(1/2)-1

eq2 = 

solve(-1/(1 - (Y - 4/5)^2)^(1/2)==1)

 
ans =
 
Empty sym: 0-by-1
 

figure
fplot(eq2,[-0.5 2])
grid
ylim([-25, 5])

solve(-1/(1 - (Y - 4/5)^2)^(1/2)==-1)

ans = 

.