Eliminate the Parameter

[mynamesmurph]

x=cos³t
y=sin³t

Any hints?

 

[Deleted member 4993]

x=cos³t
y=sin³t

Any hints?

\(\displaystyle \\\ \displaystyle{x^{\frac{2}{3}} \ = \ ?}\)


\(\displaystyle \\\ \displaystyle{y^{\frac{2}{3}} \ = \ ?}\)

 

[mynamesmurph]

Like this?

x^2/3=(cos³t)<sup>2/3

y2/3</sup>=(sin³t)<sup>2/3


3</sup>√(y2) + 3√(x²)=cos²t+sin²t

³√(y²​) + 3√(x²)=1


Edit: Is there a better way to write "nth" roots on this forum?

 

[mynamesmurph]

Was my answer correct? Sorry if it seems obvious. As usual I appreciate all of your help, you guys are great.

 

[HallsofIvy]

Like this?

x^2/3=(cos³t)<sup>2/3

y2/3</sup>=(sin³t)^2/3

Wouldn't it be better to just go ahead and write \(\displaystyle x^{2/3}= cos^2(t)\) and \(\displaystyle y^{2/3}= sin^2(t)\)

3[/SUP]√(y2) + 3√(x²)=cos²t+sin²t

³√(y²​) + 3√(x²)=1

I would probably have left it as \(\displaystyle y^{2/3}+ x^{2/3}= 1\)

Edit: Is there a better way to write "nth" roots on this forum?

Using Latex, [ tex ]\sqrt[n]{x}[ tex ], without the spaces, gives \(\displaystyle \sqrt[n]{x}\).

 

[Deleted member 4993]

Like this?

x^2/3=(cos³t)<sup>2/3

y2/3</sup>=(sin³t)<sup>2/3


3</sup>√(y2) + 3√(x²)=cos²t+sin²t

³√(y²​) + 3√(x²)=1


Edit: Is there a better way to write "nth" roots on this forum?

If you meant:

\(\displaystyle \displaystyle{x^{\frac{2}{3}} \ + \ y^{\frac{2}{3}} \ = \ 1}\) ..... then yes it is correct.

for simple expressions, I find it writing in ASCII mode is best. For example, your equation is best written as (for me):

x^(2/3) + y^(2/3) = 1

I have given you one example above as to how it could be written in LaTex. Another example would be:

\(\displaystyle \displaystyle{\ \sqrt[3]{x^2} \ + \ \sqrt[3]{y^2} \ = \ 1}\)

Again, for my taste, LaTex takes too much time!!!