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Find a rectangular-coordinate equation for the curve by eliminating the parameter. x=cos^3(t)  y=sin^3(t)   o <= t <= 2pi 

Respuesta :

LammettHash
[tex]x=\cos^3t\implies x^{2/3}=(\cos^3t)^{2/3}=\cos^2t[/tex]

SImilarly,

[tex]y=\sin^3t\implies y^{2/3}=\sin^2t[/tex]

So recalling that [tex]\cos^2t+\sin^2t=1[/tex], you end up with the rectangular form

[tex]x^{2/3}+y^{2/3}=1[/tex]

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