如何将参数方程的t消去,化为普通方程x=r(3cost+cos3t)y=r(3sint-sin3t)

Question

如何将参数方程的t消去,化为普通方程x=r(3cost+cos3t) y=r(3sint-sin3t)

Answer 1

因为sin3t=3sint-4(sint)^3,cos3t=4(cost)^3-3cost
所以：3sint-sin3t=4(sint)^3；3cost+cos3t=4(cost)^3
则,x=4r(cost)^3；y=4r(sint)^3
===> (cost)^3=x/4r；(sint)^3=y/4r
===> (cost)^2=(x/4r)^(2/3)；(sint)^2=(y/4r)^(2/3)
===> (x/4r)^(2/3)+(y/4r)^(2/3)=1