MaplePrimes - answers and comments on Question, how to convert a parametric equations back to in terms of x and y with maple?

eliminate

Preben Alsholm — Fri, 07 Dec 2012 20:01:14 Z

There is 'eliminate', which you could try. However I found the following slightly neater:

restart;
eq1,eq2:=x = a*(3*cos(t) - cos(3*t)),y = a*(3*sin(t) - sin(3*t));
sys := [eq1,eq2]:
expand(sys);
sys1:=subs(cos(t)=c,sin(t)=s,%);
solve(sys1,{s,c});
eq:=subs(%,s^2+c^2=1);
indets(eq,specfunc(anything,RootOf));
alias(q=op(%));
eq;
normal((lhs-rhs)(%));
EQ:=simplify(numer(%));
EQA:=[allvalues(EQ)];
plots:-implicitplot(eval(EQA,a=1),x=-3..3,y=-4..4,grid=[50,50],gridrefine=1);
plot(eval([rhs(eq1),rhs(eq2),t=-Pi..Pi],a=1));

By eliminate command

Markiyan Hirnyk — Fri, 07 Dec 2012 20:15:28 Z

Download eliminate.mw

Another way

Kitonum — Fri, 07 Dec 2012 22:55:22 Z

restart;

with(RealDomain):

sys := {x = expand(a*(3*cos(t) - cos(3*t))), y = simplify(expand(a*(3*sin(t) - sin(3*t))))};

subs(sin(t)=solve(sys[2], sin(t)), subs(cos(t)=sqrt(1-sin(t)^2), sys[1]));

eq:=subs(y=abs(y), simplify(lhs(%)^2=rhs(%)^2)) ;

a:=1: plots[implicitplot](eq, x=-4..4, y=-4..4, thickness=2, numpoints=10000);

Comparison with the answer by Preben

Markiyan Hirnyk — Fri, 07 Dec 2012 20:18:28 Z

screen201.docx

Comparison with one of the outputs of

Markiyan Hirnyk — Fri, 07 Dec 2012 21:59:46 Z

Output

Markiyan Hirnyk — Fri, 07 Dec 2012 23:00:20 Z