Find a Cartesian equation relating x and y corresponding to the parametric equations
x=5sin(5 t) y=9cos(5 t)
Write your answer in the form
P(x,y)=0
where P(x,y) is a polynomial in x and y such that the coefficient of y^2 is 25.

Question

Find a Cartesian equation relating x and y corresponding to the parametric equations
x=5sin(5 t)  y=9cos(5 t)
Write your answer in the form
P(x,y)=0
where P(x,y) is a polynomial in x and y such that the coefficient of y^2 is 25.

anonymous · Answer

x^2+(25y^2/81)-1 this is the answer I got :/

amistre64 · Answer

it does seem rather elliptic doesnt it ...

anonymous · Answer

Thats what I did, I used the ellipse formula  but I don't know where I'm going wrong.

amistre64 · Answer

r cos(t) = 5 sin(5t)
r sin(t) = 9 cos(5t)
$$r^2 = \sqrt{25sin^2(5t)+81cos^2(5t)}$$
hmmm

amistre64 · Answer

got a spurious ^2 on that last r

anonymous · Answer

wait where did you get the r, I thought I just had to get "rid" of my t variable by squaring both side and using the unit circle formula,

amistre64 · Answer

just trying to recall a few things is all

amistre64 · Answer

if we unparameterize it, we get

x = 5 sin(5t)

arcsin(x/5)/5 = t

y = 9 cos(5 arcsin(x/5)/5)

y = 9 cos(arcsin(x/5))

amistre64 · Answer

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