ROSECODE 207
Trigonometric equations
Solve in real variables:
sin(x)^2+cos(y)^2=y^2
sin(y)^2+cos(x)^2=x^2
Submit all solution in lexicographic increasing way.
Answer format: (x1,y1),(x2,y2),...
Here lex. sorting means that (a,b)<(c,d) if a < c or
{a=c and b < d} You can assume that all solution is in fact rational, so submit them as x=p/q, where q>0, gcd(p,q)=1 (and not use q if x is integer).
Example:
(-1/2,0),(3/4,7)
sin(x)^2+cos(y)^2=y^2
sin(y)^2+cos(x)^2=x^2
Submit all solution in lexicographic increasing way.
Answer format: (x1,y1),(x2,y2),...
Here lex. sorting means that (a,b)<(c,d) if a < c or
{a=c and b < d} You can assume that all solution is in fact rational, so submit them as x=p/q, where q>0, gcd(p,q)=1 (and not use q if x is integer).
Example:
(-1/2,0),(3/4,7)